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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

Table of n, a(n) for n=1..40.

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.)