A097956 Primes p such that p divides 5^(p-1)/2 - 3^(p-1)/2.

7, 11, 17, 43, 53, 59, 61, 67, 71, 103, 109, 113, 127, 131, 137, 163, 173, 179, 181, 191, 197, 223, 229, 233, 239, 241, 251, 257, 283, 293, 307, 311, 317, 349, 353, 359, 367, 409, 419, 421, 431, 463, 479, 487, 491, 523, 541, 547, 557, 593, 599, 601, 607, 617

Offset

1,1

Comments

From Jianing Song, Oct 13 2022: (Start)

Rational primes that decompose in the field Q(sqrt(15)).

Primes p such that kronecker(60,p) = 1.

Primes congruent to 1, 7, 11, 17, 43, 49, 53, 59 modulo 60. (End)

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Example

7 is a term since 5^3 - 3^3 = 7*14.

Mathematica

Select[Prime[Range[150]], Divisible[5^((#-1)/2)-3^((#-1)/2), #]&] (* Harvey P. Dale, Apr 11 2018 *)

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, 2, -1)
(PARI) isA097956(p) == isprime(p) && kronecker(60, p) == 1 \\ Jianing Song, Oct 13 2022

Crossrefs

A038887, the sequence of primes that do not remain inert in the field Q(sqrt(15)), is essentially the same.

Cf. A038888 (rational primes that remain inert in the field Q(sqrt(15))).

Sequence in context: A107642 A079651 A178386 * A094104 A167513 A260891

Adjacent sequences: A097953 A097954 A097955 * A097957 A097958 A097959

Keyword

nonn,easy

Author

Cino Hilliard, Sep 06 2004

Status

approved