A330409 Semiprimes of the form p(6p - 1).

22, 51, 145, 287, 1717, 2147, 3151, 5017, 11051, 13207, 16801, 20827, 26867, 63551, 68587, 71177, 76501, 96647, 112477, 147737, 159251, 232657, 237407, 308947, 314417, 342487, 433897, 480251, 587501, 602617, 722107, 772927, 834401, 861467, 879751, 907537, 945257, 1155887, 1177051

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A049452(A158015(n)) = p(6p - 1) with p = A158015(n).

Example

A158015(1) = 2 is the smallest prime p such that 6p - 1 = 12 - 1 = 11 is also prime, whence a(1) = A049452(2) = 2*(6*2 - 1) = 22.
prime(5) = 11 is the smallest prime not in A024898 or A158015, because 6p - 1 is not a prime, therefore A049452(11) = 11*(6*11 - 1) is not in the sequence, and idem for A049452(13).
But prime(7) = 17 is in A024898 and A158015, so a(5) = A024898(A158015(5)) = A024898(17) = 17*(6*17 - 1).

Mathematica

Select[Table[p(6p-1), {p, 500}], PrimeOmega[#]==2&] (* Harvey P. Dale, Apr 27 2022 *)

Prog

(PARI) [p*(6*p-1) | p<-primes(99), isprime(6*p-1)]

Crossrefs

Cf. A024898 (6n-1 is prime), A158015 (primes), A049452 = {n(6n-1)}.

Complement of A255584 = A033570(A130800) (semiprimes (2n+1)(3n+1)) in A245365 (primes of the form n(3n-1)/2).

Sequence in context: A092221 A191279 A200880 * A111576 A277979 A177726

Adjacent sequences: A330406 A330407 A330408 * A330410 A330411 A330412

Keyword

nonn

Author

M. F. Hasler, Dec 13 2019

Status

approved