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Infinite Sequence based on Simple Rule


Arranging cards in rowsTen binary passwords (The **** and *** sequence)When setting number-sequence puzzles, is there any accepted method to prevent arbitrary solutions?Rainbow Door SequenceTwo honeycomb hints (yet another 'find the next number in the sequence')Mathemagician and a number sequenceFinding Sequence in Third SquareThe Generic Number Sequence PuzzleKeeping a ball lost foreverLong digital sequence. 16xxxxxxxxxxxxx61













12












$begingroup$


Using one simple rule, an Infinite Sequence has been developed.



First 30 terms are given. Can you continue the sequence for at least next Ten Terms?



Series continues from top left to bottom right.



$3, 31, 41, 59, 53, 89, 97, 79, 23, 43,$



$83, 79, 2, 41, 19, 97, 71, 37, 5, 97$



$59, 23, 7, 89, 3, 53, 11, 17 ,67, 79$



$textNext 10$?










share|improve this question











$endgroup$







  • 5




    $begingroup$
    please change it to 30 terms
    $endgroup$
    – Ak19
    May 26 at 11:37










  • $begingroup$
    Happy to see something different, this is a good start.
    $endgroup$
    – greenturtle3141
    May 26 at 13:01






  • 3




    $begingroup$
    Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
    $endgroup$
    – Gareth McCaughan
    May 26 at 13:22










  • $begingroup$
    Can you confirm if infinite sequence means an infinite sequence that does not repeat?
    $endgroup$
    – tom
    May 26 at 14:05











  • $begingroup$
    @tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
    $endgroup$
    – Uvc
    May 26 at 14:23















12












$begingroup$


Using one simple rule, an Infinite Sequence has been developed.



First 30 terms are given. Can you continue the sequence for at least next Ten Terms?



Series continues from top left to bottom right.



$3, 31, 41, 59, 53, 89, 97, 79, 23, 43,$



$83, 79, 2, 41, 19, 97, 71, 37, 5, 97$



$59, 23, 7, 89, 3, 53, 11, 17 ,67, 79$



$textNext 10$?










share|improve this question











$endgroup$







  • 5




    $begingroup$
    please change it to 30 terms
    $endgroup$
    – Ak19
    May 26 at 11:37










  • $begingroup$
    Happy to see something different, this is a good start.
    $endgroup$
    – greenturtle3141
    May 26 at 13:01






  • 3




    $begingroup$
    Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
    $endgroup$
    – Gareth McCaughan
    May 26 at 13:22










  • $begingroup$
    Can you confirm if infinite sequence means an infinite sequence that does not repeat?
    $endgroup$
    – tom
    May 26 at 14:05











  • $begingroup$
    @tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
    $endgroup$
    – Uvc
    May 26 at 14:23













12












12








12





$begingroup$


Using one simple rule, an Infinite Sequence has been developed.



First 30 terms are given. Can you continue the sequence for at least next Ten Terms?



Series continues from top left to bottom right.



$3, 31, 41, 59, 53, 89, 97, 79, 23, 43,$



$83, 79, 2, 41, 19, 97, 71, 37, 5, 97$



$59, 23, 7, 89, 3, 53, 11, 17 ,67, 79$



$textNext 10$?










share|improve this question











$endgroup$




Using one simple rule, an Infinite Sequence has been developed.



First 30 terms are given. Can you continue the sequence for at least next Ten Terms?



Series continues from top left to bottom right.



$3, 31, 41, 59, 53, 89, 97, 79, 23, 43,$



$83, 79, 2, 41, 19, 97, 71, 37, 5, 97$



$59, 23, 7, 89, 3, 53, 11, 17 ,67, 79$



$textNext 10$?







mathematics logical-deduction knowledge number-sequence no-computers






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited May 26 at 15:11







Uvc

















asked May 26 at 10:58









UvcUvc

1,162119




1,162119







  • 5




    $begingroup$
    please change it to 30 terms
    $endgroup$
    – Ak19
    May 26 at 11:37










  • $begingroup$
    Happy to see something different, this is a good start.
    $endgroup$
    – greenturtle3141
    May 26 at 13:01






  • 3




    $begingroup$
    Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
    $endgroup$
    – Gareth McCaughan
    May 26 at 13:22










  • $begingroup$
    Can you confirm if infinite sequence means an infinite sequence that does not repeat?
    $endgroup$
    – tom
    May 26 at 14:05











  • $begingroup$
    @tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
    $endgroup$
    – Uvc
    May 26 at 14:23












  • 5




    $begingroup$
    please change it to 30 terms
    $endgroup$
    – Ak19
    May 26 at 11:37










  • $begingroup$
    Happy to see something different, this is a good start.
    $endgroup$
    – greenturtle3141
    May 26 at 13:01






  • 3




    $begingroup$
    Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
    $endgroup$
    – Gareth McCaughan
    May 26 at 13:22










  • $begingroup$
    Can you confirm if infinite sequence means an infinite sequence that does not repeat?
    $endgroup$
    – tom
    May 26 at 14:05











  • $begingroup$
    @tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
    $endgroup$
    – Uvc
    May 26 at 14:23







5




5




$begingroup$
please change it to 30 terms
$endgroup$
– Ak19
May 26 at 11:37




$begingroup$
please change it to 30 terms
$endgroup$
– Ak19
May 26 at 11:37












$begingroup$
Happy to see something different, this is a good start.
$endgroup$
– greenturtle3141
May 26 at 13:01




$begingroup$
Happy to see something different, this is a good start.
$endgroup$
– greenturtle3141
May 26 at 13:01




3




3




$begingroup$
Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
$endgroup$
– Gareth McCaughan
May 26 at 13:22




$begingroup$
Can you confirm that 51 is really correct and not a typo for, say, 53 or 61?
$endgroup$
– Gareth McCaughan
May 26 at 13:22












$begingroup$
Can you confirm if infinite sequence means an infinite sequence that does not repeat?
$endgroup$
– tom
May 26 at 14:05





$begingroup$
Can you confirm if infinite sequence means an infinite sequence that does not repeat?
$endgroup$
– tom
May 26 at 14:05













$begingroup$
@tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
$endgroup$
– Uvc
May 26 at 14:23




$begingroup$
@tom..if you mean, cyclic..it is not..Sequence is not finite..of course numbers can repeat as you can see in the numbers given.
$endgroup$
– Uvc
May 26 at 14:23










1 Answer
1






active

oldest

votes


















15












$begingroup$

The next terms are:




13, 23, 47, 5, 23, 31, 17, 53, 59, 11




Because




These are the primes found in pairs of digits of $pi$.


31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
|| | | | ||| | | | | | |||| | | | | | | | | | || ||
3|41 | 53 89|| 23 43 | 79 02 41|71 37 05 97 59 |07 89 03 53 11| 67|
31 59 97| 83 19| 23 17 79
79 97






share|improve this answer











$endgroup$












  • $begingroup$
    @florian..excellent!!
    $endgroup$
    – Uvc
    May 26 at 15:35










  • $begingroup$
    Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
    $endgroup$
    – Florian F
    May 26 at 15:39











  • $begingroup$
    I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
    $endgroup$
    – Uvc
    May 26 at 15:44










  • $begingroup$
    It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
    $endgroup$
    – Uvc
    May 27 at 1:10










  • $begingroup$
    The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
    $endgroup$
    – Florian F
    May 27 at 12:44











Your Answer








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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









15












$begingroup$

The next terms are:




13, 23, 47, 5, 23, 31, 17, 53, 59, 11




Because




These are the primes found in pairs of digits of $pi$.


31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
|| | | | ||| | | | | | |||| | | | | | | | | | || ||
3|41 | 53 89|| 23 43 | 79 02 41|71 37 05 97 59 |07 89 03 53 11| 67|
31 59 97| 83 19| 23 17 79
79 97






share|improve this answer











$endgroup$












  • $begingroup$
    @florian..excellent!!
    $endgroup$
    – Uvc
    May 26 at 15:35










  • $begingroup$
    Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
    $endgroup$
    – Florian F
    May 26 at 15:39











  • $begingroup$
    I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
    $endgroup$
    – Uvc
    May 26 at 15:44










  • $begingroup$
    It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
    $endgroup$
    – Uvc
    May 27 at 1:10










  • $begingroup$
    The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
    $endgroup$
    – Florian F
    May 27 at 12:44















15












$begingroup$

The next terms are:




13, 23, 47, 5, 23, 31, 17, 53, 59, 11




Because




These are the primes found in pairs of digits of $pi$.


31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
|| | | | ||| | | | | | |||| | | | | | | | | | || ||
3|41 | 53 89|| 23 43 | 79 02 41|71 37 05 97 59 |07 89 03 53 11| 67|
31 59 97| 83 19| 23 17 79
79 97






share|improve this answer











$endgroup$












  • $begingroup$
    @florian..excellent!!
    $endgroup$
    – Uvc
    May 26 at 15:35










  • $begingroup$
    Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
    $endgroup$
    – Florian F
    May 26 at 15:39











  • $begingroup$
    I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
    $endgroup$
    – Uvc
    May 26 at 15:44










  • $begingroup$
    It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
    $endgroup$
    – Uvc
    May 27 at 1:10










  • $begingroup$
    The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
    $endgroup$
    – Florian F
    May 27 at 12:44













15












15








15





$begingroup$

The next terms are:




13, 23, 47, 5, 23, 31, 17, 53, 59, 11




Because




These are the primes found in pairs of digits of $pi$.


31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
|| | | | ||| | | | | | |||| | | | | | | | | | || ||
3|41 | 53 89|| 23 43 | 79 02 41|71 37 05 97 59 |07 89 03 53 11| 67|
31 59 97| 83 19| 23 17 79
79 97






share|improve this answer











$endgroup$



The next terms are:




13, 23, 47, 5, 23, 31, 17, 53, 59, 11




Because




These are the primes found in pairs of digits of $pi$.


31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
|| | | | ||| | | | | | |||| | | | | | | | | | || ||
3|41 | 53 89|| 23 43 | 79 02 41|71 37 05 97 59 |07 89 03 53 11| 67|
31 59 97| 83 19| 23 17 79
79 97







share|improve this answer














share|improve this answer



share|improve this answer








edited May 26 at 17:07

























answered May 26 at 15:32









Florian FFlorian F

9,93412462




9,93412462











  • $begingroup$
    @florian..excellent!!
    $endgroup$
    – Uvc
    May 26 at 15:35










  • $begingroup$
    Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
    $endgroup$
    – Florian F
    May 26 at 15:39











  • $begingroup$
    I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
    $endgroup$
    – Uvc
    May 26 at 15:44










  • $begingroup$
    It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
    $endgroup$
    – Uvc
    May 27 at 1:10










  • $begingroup$
    The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
    $endgroup$
    – Florian F
    May 27 at 12:44
















  • $begingroup$
    @florian..excellent!!
    $endgroup$
    – Uvc
    May 26 at 15:35










  • $begingroup$
    Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
    $endgroup$
    – Florian F
    May 26 at 15:39











  • $begingroup$
    I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
    $endgroup$
    – Uvc
    May 26 at 15:44










  • $begingroup$
    It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
    $endgroup$
    – Uvc
    May 27 at 1:10










  • $begingroup$
    The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
    $endgroup$
    – Florian F
    May 27 at 12:44















$begingroup$
@florian..excellent!!
$endgroup$
– Uvc
May 26 at 15:35




$begingroup$
@florian..excellent!!
$endgroup$
– Uvc
May 26 at 15:35












$begingroup$
Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
$endgroup$
– Florian F
May 26 at 15:39





$begingroup$
Thanks! It's the 3 numbers 31,41,59 that gave it away. After that it was a piece of pie.
$endgroup$
– Florian F
May 26 at 15:39













$begingroup$
I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
$endgroup$
– Uvc
May 26 at 15:44




$begingroup$
I could have made it tougher ...but I want to make it only slightly complex and a series not to be found in oeis...opens up for so many avenues of further research into this fascinating field
$endgroup$
– Uvc
May 26 at 15:44












$begingroup$
It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
$endgroup$
– Uvc
May 27 at 1:10




$begingroup$
It would be nice to examine the prime gaps and frequency of various primes generated via this method through computer calculations.
$endgroup$
– Uvc
May 27 at 1:10












$begingroup$
The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
$endgroup$
– Florian F
May 27 at 12:44




$begingroup$
The digits of pi being practically random, the frequency of each prime should be constant at 1 occurrence everu 100 digits.
$endgroup$
– Florian F
May 27 at 12:44

















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