A099722 - OEIS

%I #16 Jun 03 2020 10:22:07

%S 11,17,23,41,47,67,83,103,157,257,277,3407,3517,3547

%N From a 2-dimensional walk involving primes.

%C Start with 7 in the center cell. Rules: Write prime(n-1) in a cell and,

%C if Prime(n-1) == 1 mod 5, then move to upper cell, append prime(n) to the cell.

%C if Prime(n-1) == 2 mod 5, then move to right cell, append prime(n) to the cell.

%C if Prime(n-1) == 3 mod 5, then move to lower cell, append prime(n) to the cell.

%C if Prime(n-1) == 4 mod 5, then move to left cell, append prime(n) to the cell.

%C Sequence gives sequence of primes appearing in the cell to the right of center cell.

%C There are no more terms below 10^10. But two-dimensional random walks are recurrent, so this sequence is heuristically infinite. - _Charles R Greathouse IV_, Oct 18 2011

%C No more terms up to 10^12. - _Charles R Greathouse IV_, May 04 2020

%C No more terms up to 10^13. The associated position after 9999999999971 is (-3312, -57946). - _Charles R Greathouse IV_, May 29 2020

%e .................. 13 ...... 13 ......... 13 .............. 13 .................

%e 7 -> 7 : 11 -> 7 : 11 -> 7 : 11,17 -> 7 : 11,17 : 19 -> 7 : 11,17,23 : 19 -> ...

%o (PARI) upto(lim)=my(x=-1,y=0,p=7);forprime(q=11,lim,if(p%5>2,if(p%5==3,y--,x--),if(p%5==1,y++,x++));if(!x&&!y,print1(q", "));p=q) \\ _Charles R Greathouse IV_, Oct 18 2011

%Y Cf. A096447.

%K nonn,more

%O 1,1

%A _Yasutoshi Kohmoto_, Nov 06 2004

%E a(8)-a(14) from _Sean A. Irvine_, Oct 18 2011