

A114439


Indices of semiprime pentagonal numbers.


1



4, 5, 6, 10, 13, 14, 29, 34, 38, 41, 46, 53, 58, 73, 86, 94, 101, 106, 109, 118, 134, 149, 181, 206, 214, 218, 226, 233, 254, 274, 281, 293, 314, 326, 349, 394, 398, 401, 409, 421, 449, 454, 458, 461, 478, 538, 541, 566, 569, 613, 626, 634, 661, 673, 694
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k1) or k*((3*k1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k1)/2 prime] or [k/2 prime and 3*k1 prime]. A115709 is pentagonal numbers (A000326) whose digit reversal is a semiprime (A001358).


LINKS

Table of n, a(n) for n=1..55.
Eric Weisstein's World of Mathematics, Pentagonal Number.


FORMULA

{a(n)} = {k such that A001222(A000326(k)) = 2}. {a(n)} = {k such that k*(3*k1)/2 has exactly 2 prime factors}. {a(n)} = {k such that A000326(k) is an element of A001358}.


EXAMPLE

a(1) = 4 because P(4) = PentagonalNumber(4) = 4*(3*4 1)/2 = 22 = 2 * 11 is semiprime.
a(2) = 5 because P(5) = 5*(3*5 1)/2 = 35 = 5 * 7 is semiprime.
a(7) = 29 because P(29) = 29*(3*29 1)/2 = 1247 = 29 * 43 is semiprime.
a(8) = 34 because P(34) = 34*(3*34 1)/2 = 1717 = 17 * 101 is semiprime.
a(17) = 101 because P(101) = 101*(3*101 1)/2 = 15251 = 101 * 151 is semiprime.


CROSSREFS

Cf. A000326, A001222, A001358, A115709.
Sequence in context: A327223 A143833 A186808 * A310570 A271146 A079257
Adjacent sequences: A114436 A114437 A114438 * A114440 A114441 A114442


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 14 2006


EXTENSIONS

More terms from Giovanni Resta, Jun 14 2016


STATUS

approved



