A179282 Numbers n such that 2^n-2 and 2^n+2 are not squarefree.

1, 22, 31, 64, 79, 91, 106, 111, 148, 151, 190, 205, 211, 232, 235, 271, 274, 311, 316, 331, 341, 358, 391, 400, 442, 451, 466, 484, 511, 526, 547, 551, 568, 571, 610, 613, 631, 652, 658, 667, 691, 694, 703, 736, 751, 760, 771, 778, 811, 820, 859, 862, 871, 904

Offset

1,2

Comments

Most (not all) of the terms are of the form:

x^2-y^2, for x>y>0.

31=16^2-15^2,

64=10^2-6^2=17^2-15^2,

79=40^2-39^2,

91=10^2-3^2=46^2-45^2,

111=20^2-17^2=56^2-55^2,

148=11^2-3^3=38^2-36^2,

151=76^2-75^2,

205=23^2-18^2=103^2-102^2,

211=106^2-105^2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..62

David A. Corneth, More terms (this file might miss terms below 10^5, but listed terms are definetely terms)

Example

2^22-2=2*7^2*127*337, 2^22+2=2*3^2*43*5419.

Mathematica

Select[Range@211, !(SquareFreeQ[2^#-2]||SquareFreeQ[2^#+2])&]

Prog

(PARI) isok(n) = !issquarefree(2^n-2) && !issquarefree(2^n+2); \\ Michel Marcus, Oct 04 2019

Crossrefs

Cf. A005117, A000918 (2^n-2), A052548 (2^n+2).

Sequence in context: A092215 A239431 A335348 * A106555 A106557 A142347

Adjacent sequences: A179279 A179280 A179281 * A179283 A179284 A179285

Keyword

nonn,hard

Author

Vladimir Joseph Stephan Orlovsky, Mar 22 2011

Extensions

a(14)-a(30) from D. S. McNeil, Mar 23 2011

a(31)-a(54) from Amiram Eldar, Oct 04 2019

Status

approved