A097957 Primes p such that p divides 5^((p-1)/2) + 4^((p-1)/2).

3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 433, 443, 457, 463, 467, 487, 503, 523, 547, 557, 563, 577, 587

Offset

1,1

Comments

Also odd primes congruent to {2, 3} mod 5, or primes with last digit 3 or 7. - Alexander Adamchuk, Nov 02 2006

5 is not a square mod p. - Michael Somos, Aug 15 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = A003631(n-1). - Alexander Adamchuk, Nov 02 2006

Example

5^3 + 4^3 = 7*27

Mathematica

Select[Prime[Range[120]], Divisible[5^((#-1)/2)+4^((#-1)/2), #]&] (* Harvey P. Dale, Feb 25 2013 *)

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", "))) }
(PARI) {a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( 20, m )== -1, cnt++ )); m} /* Michael Somos, Aug 15 2012 */

Crossrefs

Cf. A003631 = Primes congruent to {2, 3} mod 5.

Sequence in context: A034914 A034913 A040148 * A071774 A019403 A045422

Adjacent sequences: A097954 A097955 A097956 * A097958 A097959 A097960

Keyword

nonn,easy

Author

Cino Hilliard, Sep 06 2004

Extensions

Definition clarified by Harvey P. Dale, Feb 25 2013

Status

approved