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A382811

Integers k such that d*2^k - 1 is prime for some divisor d of k.

2, 3, 4, 5, 6, 7, 10, 12, 13, 16, 17, 18, 19, 21, 28, 30, 31, 36, 42, 46, 54, 60, 61, 63, 75, 81, 88, 89, 99, 102, 104, 106, 107, 108, 115, 123, 126, 127, 132, 133, 204, 214, 216, 225, 249, 264, 270, 286, 304, 306, 324, 330, 342, 352, 362, 384, 390

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..161

EXAMPLE

4 is in the sequence because 2*2^4 - 1 = 31 is prime for divisor d = 2 of k = 4.

MAPLE

filter:= proc(k) ormap(d -> isprime(d*2^k-1), numtheory:-divisors(k)) end proc:

select(filter, [$1..700]); # Robert Israel, Apr 25 2025

MATHEMATICA

q[k_] := AnyTrue[Divisors[k], PrimeQ[#*2^k - 1] &]; Select[Range[400], q] (* Amiram Eldar, Apr 16 2025 *)

PROG

(Magma) [k: k in [1..400] | not #[d: d in Divisors(k) | IsPrime(d*2^k-1)] eq 0];

(PARI) isok(k) = fordiv(k, d, if (ispseudoprime(d*2^k-1), return(1))); \\ Michel Marcus, Apr 16 2025

CROSSREFS

Supersequence of A000043, A002234.

Sequence in context: A319975 A307625 A165722 * A383043 A082400 A072993

Adjacent sequences: A382808 A382809 A382810 * A382812 A382813 A382814

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Apr 15 2025

STATUS

approved

URL: https://oeis.org/A382811

⇱ A382811 - OEIS