Voozh

A389853

Numbers k such that both 2^k-1 and 2^k+1 are sphenic.

14, 29, 47, 53, 71, 73, 179, 277, 311, 349, 353, 599, 613, 643, 1117, 1123

OFFSET

1,1

LINKS

EXAMPLE

14 is a term: 2^14-1 = 16383 = 3*43*127 and 2^14+1 = 16385 = 5*29*113.

MAPLE

q:= n-> andmap(x-> ifactors(x)[2][.., 2]=[1$3], [2^n-1, 2^n+1]):

select(q, [$1..200])[]; # Alois P. Heinz, Oct 17 2025

MATHEMATICA

Select[Range[180], AllTrue[2^# + {-1, 1}, And[SquareFreeQ[#], PrimeNu[#] == 3] &] &]

CROSSREFS

Cf. A000051, A000225, A007304, A092558 (both 2^k-1 and 2^k+1 are semiprimes).

KEYWORD

nonn,hard,more

AUTHOR

EXTENSIONS

a(8)-a(16) from Amiram Eldar, Oct 17 2025

STATUS

approved

URL: https://oeis.org/A389853