A382887 Numbers k such that (k*2^d + 1)*(d*2^k + 1) is semiprime for some divisor d of k.

1, 2, 8, 12, 30, 51, 63, 141, 201, 209, 534, 4713, 5795, 6611, 7050, 18496, 24105, 32292, 32469, 52782, 59656, 80190, 90825

Offset

1,2

Comments

a(24) > 10^5. - Michael S. Branicky, Apr 08 2025

Links

Table of n, a(n) for n=1..23.

Example

12 is in this sequence because (12*2^3 + 1)*(3*2^12 + 1) = 97*12289 is semiprime for divisor 3 of 12.

Prog

(Magma) [n: n in [1..1000] | not #[d: d in Divisors(n) | IsPrime(d*2^n+1) and IsPrime(n*2^d+1)] eq 0];
(Python)
from itertools import count, islice
from sympy import isprime, divisors
def A382887_gen(): # generator of terms
    yield from filter(lambda k:any(isprime((k<<d)+1) and isprime((d<<k)+1) for d in divisors(k, generator=True)), count(1))
A382887_list = list(islice(A382887_gen(), 10)) # Chai Wah Wu, Apr 15 2025
(PARI) isok(k) = fordiv(k, d, if (ispseudoprime(k*2^d+1) && ispseudoprime(d*2^k+1), return(1))); \\ Michel Marcus, Apr 16 2025

Crossrefs

Supersequence of A005849.

Cf. A001358, A002064, A382646.

Sequence in context: A257082 A265736 A047174 * A048074 A126775 A306898

Adjacent sequences: A382884 A382885 A382886 * A382888 A382889 A382890

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Apr 07 2025

Extensions

a(10) inserted and a(15)-a(23) from Michael S. Branicky, Apr 08 2025

Status

approved