A117961 Hexagonal numbers with prime indices.

6, 15, 45, 91, 231, 325, 561, 703, 1035, 1653, 1891, 2701, 3321, 3655, 4371, 5565, 6903, 7381, 8911, 10011, 10585, 12403, 13695, 15753, 18721, 20301, 21115, 22791, 23653, 25425, 32131, 34191, 37401, 38503, 44253, 45451, 49141, 52975, 55611

Offset

1,1

Comments

See also: A034953 Triangular numbers (A000217) with prime indices. A001248 Squares of primes. A116995 Pentagonal numbers with prime indices. A000384 Hexagonal numbers: n(2n-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.

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = A000040(n)*(2*A000040(n)-1). a(n) = A000384(prime(n)). a(n) = number of divisors of 12^(prime(n)-1) = A000005(A001021(A000040(n)-1)).

Mathematica

With[{hex=Table[n(2n-1), {n, 250}]}, Flatten[Table[Take[hex, {Prime[n]}], {n, 40}]]] (* Harvey P. Dale, Dec 04 2011 *)

Crossrefs

Cf. A000005, A000040, A000384, A001021, A034953, A001248, A116995.

Sequence in context: A378796 A197160 A182420 * A327769 A318482 A095122

Adjacent sequences: A117958 A117959 A117960 * A117962 A117963 A117964

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Apr 05 2006

Status

approved