

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
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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^t1) 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^n1) 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

JuriStepan Gerasimov, Apr 30 2016


STATUS

approved



