A242777 Primes p such that neither 2^p - 2 nor 2^p + 2 is squarefree.

31, 79, 151, 211, 271, 311, 331, 547, 571, 613, 631, 691, 751, 811, 859, 991, 1021, 1051, 1171

Offset

1,1

Comments

Primes p such that p-1 is in A187965. In particular, this sequence is infinite since all primes congruent to 31 mod 60 (79 mod 156, 111 mod 220, ...) are here. - Jianing Song, Jan 20 2021

Links

Table of n, a(n) for n=1..19.

Example

31 is in this sequence because 2^31 - 2 is divisible by 3^2 and 2^31 + 2 by 5^2.

Mathematica

Select[Prime[Range[50]], ! SquareFreeQ[2^# - 2] && ! SquareFreeQ[2^# + 2] &] (* Bruno Berselli, May 29 2014 *)
Select[Prime[Range[50]], NoneTrue[2^#+{2, -2}, SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2018 *)

Prog

(Magma) [n: n in [2..250] | IsPrime(n) and not IsSquarefree(2^n - 2) and not IsSquarefree(2^n + 2)];
(PARI) is(n)=isprime(n) && !issquarefree(2^n-2) && !issquarefree(2^n+2) \\ Charles R Greathouse IV, May 29 2014
(Sage) [p for p in primes(250) if not is_squarefree(2^p-2) and not is_squarefree(2^p+2)] # Bruno Berselli, May 29 2014

Crossrefs

Cf. A013929, A187965.

Sequence in context: A033220 A139855 A139901 * A252231 A044169 A044550

Adjacent sequences: A242774 A242775 A242776 * A242778 A242779 A242780

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, May 22 2014

Extensions

Edited by Jon E. Schoenfield, May 25 2014

More terms added (based on terms in A187965) by Jianing Song, Jan 20 2021

a(19) from Jinyuan Wang, Feb 15 2021

Status

approved