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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]
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LINKS
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Table of n, a(n) for n=1..14.
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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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Cf. A096447.
Sequence in context: A063638 A141250 A096454 * A031505 A094524 A098412
Adjacent sequences: A099719 A099720 A099721 * A099723 A099724 A099725
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KEYWORD
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nonn,more,changed
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AUTHOR
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Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Nov 06 2004
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EXTENSIONS
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a(8)-a(14) from Sean A. Irvine, Oct 18 2011
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STATUS
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approved
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