cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A097956 #24 Oct 13 2022 13:57:08
%S A097956 7,11,17,43,53,59,61,67,71,103,109,113,127,131,137,163,173,179,181,
%T A097956 191,197,223,229,233,239,241,251,257,283,293,307,311,317,349,353,359,
%U A097956 367,409,419,421,431,463,479,487,491,523,541,547,557,593,599,601,607,617
%N A097956 Primes p such that p divides 5^(p-1)/2 - 3^(p-1)/2.
%C A097956 From _Jianing Song_, Oct 13 2022: (Start)
%C A097956 Rational primes that decompose in the field Q(sqrt(15)).
%C A097956 Primes p such that kronecker(60,p) = 1.
%C A097956 Primes congruent to 1, 7, 11, 17, 43, 49, 53, 59 modulo 60. (End)
%H A097956 Harvey P. Dale, <a href="/A097956/b097956.txt">Table of n, a(n) for n = 1..1000</a>
%H A097956 <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%e A097956 7 is a term since 5^3 - 3^3 = 7*14.
%t A097956 Select[Prime[Range[150]],Divisible[5^((#-1)/2)-3^((#-1)/2),#]&] (* _Harvey P. Dale_, Apr 11 2018 *)
%o A097956 (PARI) \\ s = +-1, d=diff
%o A097956 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, ", "))) }
%o A097956 ptopm1d2(1000, 5, 2, -1)
%o A097956 (PARI) isA097956(p) == isprime(p) && kronecker(60, p) == 1 \\ _Jianing Song_, Oct 13 2022
%Y A097956 A038887, the sequence of primes that do not remain inert in the field Q(sqrt(15)), is essentially the same.
%Y A097956 Cf. A038888 (rational primes that remain inert in the field Q(sqrt(15))).
%K A097956 nonn,easy
%O A097956 1,1
%A A097956 _Cino Hilliard_, Sep 06 2004