A122492 Semiprimes k such that 1 + 2k + 3k^2 is also semiprime.

4, 6, 9, 10, 15, 21, 22, 33, 35, 57, 69, 77, 82, 86, 95, 111, 123, 134, 143, 146, 161, 183, 202, 203, 209, 218, 219, 221, 249, 262, 267, 298, 299, 302, 314, 321, 323, 326, 329, 334, 335, 339, 341, 417, 422, 446, 454, 471, 489, 515, 543, 551, 554, 562, 566, 573

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3500

Example

k = 4 = 2*2 (semiprime) is a term because 1 + 2k + 3k^2 = 57 = 3*19 (semiprime), etc.

Mathematica

Select[Range[600], PrimeOmega[#]==PrimeOmega[1+2#+3#^2]==2&] (* Harvey P. Dale, Nov 04 2023 *)

Prog

(Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..600] | IsSemiprime(n) and IsSemiprime(1+2*n+3*n^2)]; // Vincenzo Librandi, Jan 09 2019

Crossrefs

Cf. A086285 (numbers k such that 1 + 2k + 3k^2 is prime).

Sequence in context: A137167 A181564 A119961 * A178378 A133234 A111206

Adjacent sequences: A122489 A122490 A122491 * A122493 A122494 A122495

Keyword

nonn

Author

Zak Seidov, Oct 20 2006

Status

approved