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Search: id:A131652
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| A131652 |
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Primes p for which sum_{1 <= n < p} (n!|p) == 0 (mod p), where (n!|p) is the Legendre symbol. |
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1
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| 3, 7, 59, 83, 89, 113, 367, 379, 467, 593, 907, 1217, 1699, 1777, 1951, 2287, 2383, 2999, 3019, 3121, 4271, 4817, 5839, 6481, 6569, 6719, 9479, 9743, 14867, 16103, 17443, 17839, 18523, 19841, 21803, 22003, 22147, 24151, 25391, 26399
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..117.
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EXAMPLE
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7 is a term in the sequence because (1!|7) + (2!|7) + (3!|7) + (4!|7) + (5!|7) + (6!|7) = (1|7) + (2|7) + (6|7) + (24|7) + (120|7) + (720|7) = (1|7) + (2|7) + (6|7) + (3|7) + (1|7) + (6|7) = 1+1+(-1)+(-1)+1+(-1) = 0.
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MATHEMATICA
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fQ[n_] := Block[{p = Prime@n, s = 0, k = t = 1}, While[k < p, t = Mod[t*k, p]; k++; s = s + JacobiSymbol[t, p]]; s == 0]; Do[m = n; If[fQ@n, Print@Prime@n], {n, 4000}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
fQ[p_] := Mod[ Sum[ JacobiSymbol[ k!, p], {k, p - 1}], p] == 0; Do[ If[ fQ@ Prime@ n, Print@ Prime@ n], {n, 3008}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
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CROSSREFS
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Sequence in context: A144030 A130294 A100772 this_sequence A164895 A046859 A084289
Adjacent sequences: A131649 A131650 A131651 this_sequence A131653 A131654 A131655
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KEYWORD
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nonn
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AUTHOR
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Chris Monico (c.monico(AT)ttu.edu), Sep 10 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
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