A099722 From a 2-dimensional walk involving primes.

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

Offset: 1

Author

Yasutoshi Kohmoto, Nov 06 2004

Keywords

• nonn
• more

Comments

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

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

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

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

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

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

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

No more terms up to 10^12. - Charles R Greathouse IV, May 04 2020

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

Examples

			.................. 13 ...... 13 ......... 13 .............. 13 .................
7 -> 7 : 11 -> 7 : 11 -> 7 : 11,17 -> 7 : 11,17 : 19 -> 7 : 11,17,23 : 19 -> ...
		

Crossrefs

Cf. A096447.

Programs

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

Extensions

a(8)-a(14) from Sean A. Irvine, Oct 18 2011