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
Keywords
Examples
6 is in the sequence a term because 3*2^6 + 1 = 193 prime for divisor 3 of k = 6.
Programs
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Magma
[k: k in [1..900] | not #[d: d in Divisors(k) | IsPrime(d*2^k+1)] eq 0];
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Mathematica
q[k_] := AnyTrue[Divisors[k], PrimeQ[# * 2^k +1] &]; Select[Range[4000], q] (* Amiram Eldar, Apr 28 2025 *)
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PARI
isok(k) = fordiv(k, d, if (ispseudoprime(d*2^k+1), return(1))); return(0); \\ Michel Marcus, Apr 28 2025