A039914 -id:A039914 - cp's OEIS frontend

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.

5, 155, 505, 2755, 3421, 6805, 11341, 27721, 29755, 31861, 44309, 49505, 52211, 65791, 100171, 121451, 134321, 185329, 195805, 236681, 252505, 258571, 292139, 325469, 375155, 380071, 452255, 457651, 465805, 563249, 676505, 1041419, 1061929

Offset: 1

Derek Orr, Feb 09 2014

nonn

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

A subsequence of A165900 and A028387. - M. F. Hasler, Mar 01 2014

			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.

Cf. A237360, A039914, A002327.

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

import sympy
from sympy import isprime
{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)}

a(n) = A165900(A230026(n)). - M. F. Hasler, Mar 01 2014

A306190 a(n) = p^2 - p - 1 where p = prime(n), the n-th prime.

Original entry on oeis.org

1, 5, 19, 41, 109, 155, 271, 341, 505, 811, 929, 1331, 1639, 1805, 2161, 2755, 3421, 3659, 4421, 4969, 5255, 6161, 6805, 7831, 9311, 10099, 10505, 11341, 11771, 12655, 16001, 17029, 18631, 19181, 22051, 22649, 24491, 26405, 27721, 29755, 31861, 32579, 36289

Offset: 1

Kritsada Moomuang, Jan 28 2019

nonn

Terms are divisible by 5 iff p is of the form 10*m + 3 (A030431).

			a(3) = 19 because 5^2 - 5 - 1 = 19.

Robert Israel, Table of n, a(n) for n = 1..10000

Supersequence of A091568.
Subsequence of A028387 or A165900.
Second column of A378979.
Cf. A000040, A001248, A030431, A033879, A036689, A036690, A060800, A065479, A065488, A072055, A089241.
A039914 is an essentially identical sequence.

map(p -> p^2-p-1, [seq(ithprime(i),i=1..100)]); # Robert Israel, Mar 11 2019

Table[Prime[n]^2-Prime[n]-1, {n, 1, 100}] (* Jinyuan Wang, Feb 02 2019 *)

a(n) = {p=prime(n);p^2-p-1;} \\ Jinyuan Wang, Feb 02 2019

a(n) = A036689(n) - 1.
a(n) = A036690(n) - A072055(n).
a(n) = A060800(n) - A089241(n).
From Amiram Eldar, Nov 07 2022: (Start)
Product_{n>=1} (1 + 1/a(n)) = A065488.
Product_{n>=2} (1 - 1/a(n)) = A065479. (End)
a(n) = A033879(A001248(n)). [Deficiency of squares of primes] - Antti Karttunen, Dec 13 2024

cp's OEIS Frontend

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.

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