

A309942


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


2



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
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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^k1), g=bigomega(2^k+1)); if(f==g, print1(k, ", ")))
(MAGMA) [m:m in [2..400] &+[p[2]: p in Factorization(2^m1)] eq &+[p[2]: p in Factorization(2^m+1)]]; // Marius A. Burtea, Aug 24 2019


CROSSREFS

Cf. A000051, A000225, A046051, A054992.
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



