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A237527 Numbers n of the form p^2-p-1 = A165900(p), for prime p, such that n^2-n-1 = A165900(n) is also prime. 3

%I #14 Mar 01 2014 13:19:50

%S 5,155,505,2755,3421,6805,11341,27721,29755,31861,44309,49505,52211,

%T 65791,100171,121451,134321,185329,195805,236681,252505,258571,292139,

%U 325469,375155,380071,452255,457651,465805,563249,676505,1041419,1061929

%N Numbers n of the form p^2-p-1 = A165900(p), for prime p, such that n^2-n-1 = A165900(n) is also prime.

%C All numbers are congruent to 1 mod 10, 5 mod 10, or 9 mod 10.

%C A subsequence of A165900 and A028387. - _M. F. Hasler_, Mar 01 2014

%F a(n) = A165900(A230026(n)). - _M. F. Hasler_, Mar 01 2014

%e 5 = 3^2-3-1 (3 is prime) and 5^2-5-1 = 19 is also prime. So, 5 is a member of this sequence.

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n**2-n-1) for n in range(10**4) if isprime(n) and isprime((n**2-n-1)**2-(n**2-n-1)-1)}

%o (PARI) s=[]; forprime(p=2, 40000, n=p^2-p-1; if(isprime(n^2-n-1), s=concat(s, n))); s \\ _Colin Barker_, Feb 10 2014

%Y Cf. A237360, A039914, A002327.

%K nonn

%O 1,1

%A _Derek Orr_, Feb 09 2014

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)