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

Table of n, a(n) for n=1..16.

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).

Supersets: A262978, A294729, A389854.

Sequence in context: A257645 A046045 A132756 * A192836 A124681 A195145

Adjacent sequences: A389850 A389851 A389852 * A389854 A389855 A389856

Keyword

nonn,hard,more

Author

Michael De Vlieger, Oct 17 2025

Extensions

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

Status

approved