A372582 Numbers k such that 2*k + 3 and 3*k + 2 are semiprimes.

11, 24, 31, 44, 69, 71, 92, 99, 100, 101, 107, 108, 109, 123, 125, 128, 131, 132, 148, 160, 181, 184, 204, 207, 224, 235, 243, 245, 249, 251, 263, 267, 271, 288, 289, 297, 304, 332, 347, 348, 355, 357, 359, 360, 364, 371, 373, 380, 384, 389, 400, 420, 423, 445, 448, 449, 451, 459, 460, 465, 485

Offset

1,1

Comments

The first k where k, k + 1 and k + 2 are all terms is 99. There is no k where k, k + 1, k + 2 and k + 3 are all terms, because 3 * t + 2 is divisible by 4 for t = one of these.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 31 is a term because 2 * 31 + 3 = 65 = 5 * 13 and 3 * 31 + 2 = 95 = 5 * 19 are both semiprimes.

Maple

filter:= k -> numtheory:-bigomega(3*k+2) = 2 and numtheory:-bigomega(2*k+3) = 2:
select(filter, [$1..1000]);

Mathematica

s = {}; Do[If[2 == PrimeOmega[2*k + 3] == PrimeOmega[3*k + 2], AppendTo[s, k]], {k, 10^3}]; s

Crossrefs

Cf. A001358.

Sequence in context: A086710 A052428 A051909 * A112134 A063307 A213991

Adjacent sequences: A372578 A372580 A372581 * A372583 A372584 A372585

Keyword

nonn

Author

Zak Seidov and Robert Israel, May 05 2024

Status

approved