A114517 Numbers k such that the k-th heptagonal number is semiprime.

4, 5, 10, 13, 14, 17, 22, 26, 29, 34, 41, 46, 53, 61, 62, 73, 74, 94, 97, 101, 109, 113, 118, 122, 146, 158, 166, 173, 178, 194, 197, 218, 229, 241, 257, 262, 274, 277, 281, 298, 314, 326, 334, 353, 358, 382, 389, 397, 398, 409, 421, 454, 458, 461, 521, 538

Offset

1,1

Comments

Hep(2) = 7 is the only prime heptagonal number.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Heptagonal Number.

Eric Weisstein's World of Mathematics, Semiprime.

Formula

Numbers k such that Hep(k) = k*(5*k-3)/2 is semiprime.

Numbers k such that A000566(k) is a term of A001358.

Numbers k such that A001222(A000566(k)) = 2.

Numbers k such that A001222(k*(5*k-3)/2) = 2.

Numbers k such that [k/2 is prime and 5*k-3 is prime] or [k is prime and (5*k-3)/2 is prime].

Example

a(1) = 4 because Hep(4) = 4*(5*4-3)/2 = 34 = 2 * 17 is semiprime.
a(2) = 5 because Hep(5) = 5*(5*5-3)/2 = 55 = 5 * 11 is semiprime.
a(10) = 34 because Hep(34) = 2839 = 17 * 167 is semiprime and this is also the first iterated heptagonal semiprime Hep(34) = Hep(Hep(4)).
a(20) = 101 because Hep(101) = 25351 = 101 * 251 is semiprime [and brilliant].

Mathematica

Select[Range[700], PrimeOmega[(#(5#-3))/2]==2&] (* Harvey P. Dale, Jul 24 2011 *)

Crossrefs

Cf. A000040, A000566, A001222, A001358, A099153.

Sequence in context: A058335 A222353 A094415 * A283246 A236283 A378273

Adjacent sequences: A114514 A114515 A114516 * A114518 A114519 A114520

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 15 2006

Extensions

More terms from Harvey P. Dale, Jul 24 2011

Status

approved