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A097956
Primes p such that p divides 5^(p-1)/2 - 3^(p-1)/2.
4
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)
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
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Sep 06 2004
STATUS
approved