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A269758 Prime powers with squarefree neighbors. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)