A262978 Exponents n such that 2^n-1 and 2^n+1 are squarefree.

1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 115, 116, 118, 119

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..608

Formula

2^a(n) = A269758(n).

Example

a(4) = 5 because 2^5 - 1 = 31 and 2^5 + 1 = 33 are squarefree numbers.

Mathematica

Select[Range[120], AllTrue[2^#+{1, -1}, SquareFreeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 20 2019 *)

Prog

(Magma) [n: n in [1..120] | IsSquarefree(2^n-1) and IsSquarefree(2^n+1)];
(PARI) is(n)=issquarefree(2^n-1) && issquarefree(2^n+1) \\ Charles R Greathouse IV, May 02 2016

Crossrefs

Cf. A000961, A229303, A269758.

Sequence in context: A206285 A356449 A229303 * A112886 A282429 A111040

Adjacent sequences: A262975 A262976 A262977 * A262979 A262980 A262981

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, May 01 2016

Status

approved