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 A114439 Indices of semiprime pentagonal numbers. 2
 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*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime]. A115709 is pentagonal numbers (A000326) whose digit reversal is a semiprime (A001358). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 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*k-1)/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. MATHEMATICA Position[PolygonalNumber[5, Range], _?(PrimeOmega[#]==2&)]//Flatten (* Harvey P. Dale, Oct 02 2021 *) CROSSREFS Cf. A000326, A001222, A001358, A115709. Sequence in context: A327223 A143833 A186808 * A310570 A271146 A347806 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

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Last modified October 19 20:16 EDT 2021. Contains 348091 sequences. (Running on oeis4.)