A176972 a(n) = 7^n + 7*n + 1.

2, 15, 64, 365, 2430, 16843, 117692, 823593, 5764858, 40353671, 282475320, 1977326821, 13841287286, 96889010499, 678223072948, 4747561510049, 33232930569714, 232630513987327, 1628413597910576, 11398895185373277

Offset

0,1

Comments

This is to 7 as A176916 is to 5, A176805 is to 3, and as A176691 is to 2. This is the 7th row of the array A[k,n] = k^n + k*n + 1. The subsequence of primes begins: 2, 16843, 1977326821, no more through a(200).

The next term that is prime, for n=1390, has 1174 digits. Then there are no further prime terms through n=5000. - Harvey P. Dale, Apr 17 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (9,-15,7). [From R. J. Mathar, May 22 2010]

Formula

a(n) = 7^n + 7*n + 1 = A000420(n) + A008589(n) + 1 = A000420(n) + A016993(n).

a(n) = 7*a(n-1) - 42*(n-1) + 1, with n > 0. For n=5, a(5) = 7*2430 - 42*4 + 1 = 16843. [Bruno Berselli, May 18 2010]

From R. J. Mathar, May 22 2010: (Start)

a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).

G.f.: (-2 + 3*x + 41*x^2) / ((7*x-1)*(x-1)^2). (End)

Example

a(5) = 7^5 + 7*5 + 1 = 16843 is prime.

Mathematica

Table[7^n+7n+1, {n, 0, 20}] (* or *) LinearRecurrence[{9, -15, 7}, {2, 15, 64}, 20] (* Harvey P. Dale, Apr 17 2014 *)

Prog

(Magma) [7^n + 7*n + 1: n in [0..25]]; // Vincenzo Librandi, May 06 2011

Crossrefs

Cf. A000420, A008589, A016993, A176691, A176805, A176916.

Sequence in context: A119904 A271828 A183264 * A117393 A055206 A216614

Adjacent sequences: A176969 A176970 A176971 * A176973 A176974 A176975

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 29 2010

Extensions

First comment corrected by Harvey P. Dale, Apr 17 2014

Status

approved