A309942 Numbers k such that 2^k - 1 and 2^k + 1 have the same number of prime factors, counted with multiplicity.

2, 10, 11, 14, 21, 23, 29, 39, 47, 50, 53, 55, 63, 71, 73, 74, 75, 82, 86, 95, 101, 105, 113, 115, 121, 142, 147, 150, 167, 169, 179, 181, 182, 190, 199, 203, 209, 233, 235, 253, 277, 285, 303, 307, 311, 317, 335, 337, 339, 342, 343, 347, 349, 353, 355, 358

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

a(1) = 2: 2^2 - 1 = 3 and 2^2 + 1 are both prime,
a(2) = 10: 2^10 - 1 = 1023 = 3 * 11 * 31 and 2^10 + 1 = 1025 = 5^2 * 41 both have 3 prime factors.

Mathematica

Select[Range[200], PrimeOmega[2^# - 1 ] == PrimeOmega[2^# + 1 ] &] (* Amiram Eldar, Aug 24 2019 *)

Prog

(PARI) for(k=1, 209, my(f=bigomega(2^k-1), g=bigomega(2^k+1)); if(f==g, print1(k, ", ")))
(Magma) [m:m in [2..400]| &+[p[2]: p in Factorization(2^m-1)] eq &+[p[2]: p in Factorization(2^m+1)]]; // Marius A. Burtea, Aug 24 2019

Crossrefs

Cf. A000051, A000225, A046051, A054992, A067886.

Sequence in context: A340051 A000462 A340649 * A282093 A032930 A033293

Adjacent sequences: A309939 A309940 A309941 * A309943 A309944 A309945

Keyword

nonn

Author

Hugo Pfoertner, Aug 24 2019

Extensions

More terms from Amiram Eldar, Aug 24 2019

Status

approved