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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.
3
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
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. also A345898, A345900.
Sequence in context: A348283 A046022 A175787 * A073019 A174291 A007885
KEYWORD
nonn,hard,more,changed
AUTHOR
Michel Marcus, Jun 29 2021
EXTENSIONS
a(18) from Amiram Eldar, Jun 29 2021
STATUS
approved