A345899 Exponents d of powers of 2, q = 2^d, such that each of q-1 and q+1 is either a power of prime or a semiprime.

1, 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 31, 61, 101, 127, 167, 199, 347

Offset

1,2

Comments

a(19) > 1062, if it exists. - Amiram Eldar, Jun 29 2021

Links

Table of n, a(n) for n=1..18.

Peter Cameron, Between Fermat and Mersenne, Blog Post, October 07 2020.

Peter Cameron, Between Fermat and Mersenne, Blog Post, October 07 2020. [Local copy, with permission.]

Peter J. Cameron, Pallabi Manna, and Ranjit Mehatari, On finite groups whose power graph is a cograph, arXiv:2106.14217 [math.GR], 2021. See Theorem 1.3 (b) pp. 3-4.

Example

2^13 = 8192, and 8191 is a prime and 8193 = 3*2731 is the product of twop primes, so 13 is a term. - N. J. A. Sloane, Nov 01 2024

Prog

(PARI) isor(q) = (q==1) || isprimepower(q) || (bigomega(q)==2);
isokb(d) = my(q=2^d); isor(q-1) && isor(q+1);

Crossrefs

Cf. A000961, A001358.

Cf. also A345898, A345900.

Sequence in context: A348283 A046022 A175787 * A073019 A174291 A007885

Adjacent sequences: A345896 A345897 A345898 * A345900 A345901 A345902

Keyword

nonn,hard,more

Author

Michel Marcus, Jun 29 2021

Extensions

a(18) from Amiram Eldar, Jun 29 2021

Status

approved