A249305 Primes p such that 2^p - p^2 is not squarefree.

2, 89, 149, 151, 383, 409, 443

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 25 2014

Keywords

• nonn
• more

Comments

Sequence is infinite, containing all primes congruent to 2, 4, 89, or 115 mod 147. - Charles R Greathouse IV, Oct 28 2014

997 is also a term in this sequence. - Kevin P. Thompson, Jun 13 2022

Examples

			2 is in this sequence because 2 is prime and 2^2 - 2^2 = 0 is not squarefree.
		

Crossrefs

Cf. A005117, A024012.

Programs

Magma

[n: n in [3..269] | IsPrime(n) and not IsSquarefree(2^n - n^2)];

PARI

is(n)=isprime(n) && !issquarefree(2^n-n^2) \\ Charles R Greathouse IV, Oct 28 2014

Formula

a(n) < (21 + e)*n log n for any e > 0 and all large enough n. - Charles R Greathouse IV, Oct 28 2014

Extensions

a(5)-a(6) from Charles R Greathouse IV, Oct 28 2014

a(7) from Kevin P. Thompson, Jun 13 2022