1,1

There are no prime hexagonal numbers. The n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.

Eric Weisstein's World of Mathematics, Hexagonal Number.

Eric Weisstein's World of Mathematics, Almost Prime.

n such that hexagonal number A000384(n) is an element of A014613. n such that A001222(A000384(n)) = 4. n such that A001222(n*(2*n-1)) = 4.

a(1) = 12 because HexagonalNumber(12) = H(12) = 12*(2*12-1) = 276 = 2^2 * 3 * 23 is a 4-almost prime.

a(2) = 23 because H(23) = 23*(2*23-1) = 1035 = 3^2 * 5 * 23 is a 4-almost prime.

a(3) = 25 because H(25) = 25*(2*25-1) = 1225 = 5^2 * 7^2 is a 4-almost prime.

Cf. A000384, A001222, A014613.

Adjacent sequences: A114452 A114453 A114454 this_sequence A114456 A114457 A114458

Sequence in context: A014633 A066458 A101104 this_sequence A048992 A088783 A029756

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 14 2006