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A099722
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From a 2-dimensional walk involving primes.
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0
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11, 17, 23, 41, 47, 67, 83, 103, 157, 257, 277, 3407, 3517, 3547
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OFFSET
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1,1
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COMMENTS
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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 10^13. The associated position after 9999999999971 is (-3312, -57946). - Charles R Greathouse IV, May 29 2020
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LINKS
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EXAMPLE
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.................. 13 ...... 13 ......... 13 .............. 13 .................
7 -> 7 : 11 -> 7 : 11 -> 7 : 11,17 -> 7 : 11,17 : 19 -> 7 : 11,17,23 : 19 -> ...
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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