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 A106734 a(n) = n^3 - 7*n + 7. 3
 1, 1, 13, 43, 97, 181, 301, 463, 673, 937, 1261, 1651, 2113, 2653, 3277, 3991, 4801, 5713, 6733, 7867, 9121, 10501, 12013, 13663, 15457, 17401, 19501, 21763, 24193, 26797, 29581, 32551, 35713, 39073, 42637, 46411, 50401, 54613, 59053, 63727 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS n*a(n) + n*(n - 1)*7 = n^4. After the two units, there are 23 consecutive prime or semiprime values. See notes on primes in another cubic, A105551. Primes in this cubic include: a(3) = 13, (4) = 43, a(5) = 97, a(6) = 181, a(8) = 463, a(9) = 673, a(10) = 937, a(13) = 2113, a(17) = 4801, a(19) = 6733, a(20) = 7867, a(22) = 10501, a(26) = 17401, a(27) = 19501, a(31) = 29581, a(36) = 46411, a(39) = 59053, a(40) = 63727. Semiprimes include a(7) = 301 = 7 * 43, a(11) = 1261 = 13 * 97, a(12) = 1651 = 13 * 127, a(14) = 2653 = 7 * 379, a(15) = 3277 = 29 * 113, a(16) = 3991 = 13 * 307, a(18) = 5713 = 29 * 197, a(21) = 9121 = 7 * 1303, a(23) = 12013 = 41 * 293, a(24) = 13663 = 13 * 1051, a(28) = 21763 = 7 * 3109, a(30) = 26797 = 127 * 211, a(29) = 24193 = 13 * 1861, a(32) = 32551 = 43 * 757, a(33) = 35713 = 71 * 503, a(34) = 39073 = 41 * 953, a(35) = 42637 = 7 * 6091, a(37) = 50401 = 13 * 3877, a(38) = 54613 = 13 * 4201. There are no 3-almost primes until a(25) = 15457 = 13 * 29 * 41. - Jonathan Vos Post, May 16 2005 LINKS Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: (1-3*x+15*x^2-7*x^3)/(x-1)^4. - Harvey P. Dale, Feb 18 2018 EXAMPLE a(2) = 1, 1 + 15 = 2^4; a(3) = 13, 13 + 27 + 41 = 3^4; a(4) = 43, 43 + 57 + 71 + 85 = 4^4. MATHEMATICA Table[n^3-7n+7, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 1, 13, 43}, 40] (* Harvey P. Dale, Feb 18 2018 *) PROG (PARI) a(n) = n^3 - 7*n + 7; \\ Michel Marcus, Sep 05 2013 CROSSREFS Cf. A105551. Sequence in context: A031382 A187677 A082040 * A066465 A023262 A067260 Adjacent sequences:  A106731 A106732 A106733 * A106735 A106736 A106737 KEYWORD nonn AUTHOR Andras Erszegi (erszegi.andras(AT)chello.hu), May 14 2005 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 16 2007 STATUS approved

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Last modified March 26 14:18 EDT 2019. Contains 321497 sequences. (Running on oeis4.)