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
Keywords
Examples
k = 4 = 2*2 (semiprime) is a term because 1 + 2k + 3k^2 = 57 = 3*19 (semiprime), etc.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..3500
Crossrefs
Cf. A086285 (numbers k such that 1 + 2k + 3k^2 is prime).
Programs
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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
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Mathematica
Select[Range[600],PrimeOmega[#]==PrimeOmega[1+2#+3#^2]==2&] (* Harvey P. Dale, Nov 04 2023 *)