A269758 Prime powers with squarefree neighbors.

2, 4, 16, 32, 128, 256, 2048, 8192, 16384, 65536, 131072, 524288, 4194304, 8388608, 33554432, 67108864, 268435456, 536870912, 2147483648, 4294967296, 17179869184, 34359738368, 137438953472, 274877906944, 2199023255552, 8796093022208, 17592186044416, 70368744177664

Offset

1,1

Comments

All a(n) are powers of 2.

No terms are powers of 8. - Robert Israel, Jan 07 2019

Links

Robert Israel, Table of n, a(n) for n = 1..150

Example

2 is in this sequence because both 2 - 1 = 1 and 2 + 1 = 3 are squarefree.

Maple

map(t -> 2^t, select(t -> numtheory:-issqrfree(2^t-1) and numtheory:-issqrfree(2^t+1), [seq(seq(3*k+i, i=1..2), k=0..20)])); # Robert Israel, Jan 07 2019

Prog

(Magma) [2^n: n in [1..50] | IsSquarefree(2^n-1) and IsSquarefree(2^n+1)];

Crossrefs

Cf. A000961.

Sequence in context: A274497 A145119 A081411 * A094384 A053038 A001088

Adjacent sequences: A269755 A269756 A269757 * A269759 A269760 A269761

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 30 2016

Status

approved