A383473 Integers k such that d*2^k + 1 is prime for some divisor of k.

1, 2, 4, 6, 8, 12, 14, 15, 16, 18, 25, 30, 36, 51, 55, 63, 66, 69, 75, 81, 85, 134, 141, 162, 189, 201, 209, 220, 245, 276, 324, 408, 438, 446, 456, 534, 616, 675, 693, 726, 892, 900, 1305, 1326, 1494, 1824, 2208, 2394, 2766, 2826, 3024, 3168, 3189, 3690, 3703, 3880, 3912, 3927, 4410, 4543, 4713

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

6 is in the sequence a term because 3*2^6 + 1 = 193 prime for divisor 3 of k = 6.

Mathematica

q[k_] := AnyTrue[Divisors[k], PrimeQ[# * 2^k +1] &]; Select[Range[4000], q] (* Amiram Eldar, Apr 28 2025 *)

Prog

(Magma) [k: k in [1..900] | 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))); return(0); \\ Michel Marcus, Apr 28 2025

Crossrefs

Supersequence of A005849.

Cf. A002064, A027750, A382811.

Sequence in context: A323505 A350355 A172311 * A103829 A164530 A058817

Adjacent sequences: A383470 A383471 A383472 * A383474 A383475 A383476

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 27 2025

Status

approved