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
Examples
31 is in this sequence because 2^31 - 2 is divisible by 3^2 and 2^31 + 2 by 5^2.
Programs
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Magma
[n: n in [2..250] | IsPrime(n) and not IsSquarefree(2^n - 2) and not IsSquarefree(2^n + 2)];
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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 *)
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PARI
is(n)=isprime(n) && !issquarefree(2^n-2) && !issquarefree(2^n+2) \\ Charles R Greathouse IV, May 29 2014
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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
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
Comments