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A097955 Primes p such that p divides 5^((p-1)/2) - 2^((p-1)/2). 3
3, 13, 31, 37, 41, 43, 53, 67, 71, 79, 83, 89, 107, 151, 157, 163, 173, 191, 197, 199, 227, 239, 241, 271, 277, 281, 283, 293, 307, 311, 317, 347, 359, 373, 397, 401, 409, 431, 439, 443, 449, 467, 479, 521, 523, 547, 557, 563, 569, 587, 599, 601, 613, 631, 641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also 3 and primes p such that (p^2 - 1)/24 mod 10 = {0, 7}. - Richard R. Forberg, Aug 31 2013

Also primes p such that x^2 = 10 mod p has integer solutions, or Legendre(10, p) = 1. However, p could be irreducible but not prime in Z[sqrt(10)], especially if p = 3 or 7 mod 10. - Alonso del Arte, Dec 27 2015

Rational primes that decompose in the field Q(sqrt(10)). - N. J. A. Sloane, Dec 26 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

For p = 13, 5^6 - 2^6 =  15561 is divisible by 13, so 13 is in the sequence.

MAPLE

select(p -> isprime(p) and  10 &^ ((p-1)/2)  mod p = 1, [seq(i, i=3..1000, 2)]); # Robert Israel, Dec 28 2015

MATHEMATICA

Select[Prime[Range[100]], JacobiSymbol[10, #] == 1 &] (* Alonso del Arte, Dec 27 2015 *)

PROG

(PARI) \\ s = +-1, d=diff

ptopm1d2(n, x, d, s) = { forprime(p=3, n, p2=(p-1)/2; y=x^p2 + s*(x-d)^p2; if(y%p==0, print1(p", "))) }

ptopm1d2(1000, 5, 3, -1)

CROSSREFS

Sequence in context: A296014 A273337 A273769 * A320587 A077717 A235265

Adjacent sequences:  A097952 A097953 A097954 * A097956 A097957 A097958

KEYWORD

nonn

AUTHOR

Cino Hilliard, Sep 06 2004

STATUS

approved

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Last modified February 26 06:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)