A131652 Primes p for which Sum_{1 <= n < p} (n!|p) == 0 (mod p), where (n!|p) is the Legendre symbol.

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

Offset

1,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..117.

Example

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.

Mathematica

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, 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, Sep 17 2007 *)

Crossrefs

Sequence in context: A100772 A320724 A259266 * A213734 A185846 A239023

Adjacent sequences: A131649 A131650 A131651 * A131653 A131654 A131655

Keyword

nonn

Author

Chris Monico (c.monico(AT)ttu.edu), Sep 10 2007

Extensions

More terms from Robert G. Wilson v, Sep 17 2007

Status

approved