A195463 a(n) = 4^(n+1) + 7.

11, 23, 71, 263, 1031, 4103, 16391, 65543, 262151, 1048583, 4194311, 16777223, 67108871, 268435463, 1073741831, 4294967303, 17179869191, 68719476743, 274877906951, 1099511627783, 4398046511111, 17592186044423, 70368744177671, 281474976710663, 1125899906842631

Offset

0,1

Comments

These are the even terms of A168415. Since the odd terms of A168415 are divisible by three the primes of this sequence are the same as A104066.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Formula

a(n) = 4^(n+1) + 7.

From Alexander R. Povolotsky, Sep 19 2011: (Start)

G.f.: (11 - 32*x)/(1 - 5*x + 4*x^2).

a(n+1) = 4*a(n) - 21. (End)

a(n) = A188165(2*n+2) - 2. - Bruno Berselli, Sep 26 2011

E.g.f.: exp(x)*(4*exp(3*x) + 7). - Elmo R. Oliveira, Feb 20 2025

Mathematica

4^Range[25] + 7 (* Paolo Xausa, Feb 21 2025 *)

Prog

(PARI) a(n)=4^(n+1)+7 \\ Charles R Greathouse IV, Sep 19 2011
(Magma) [4^(n+1) + 7: n in [0..30]]; // Vincenzo Librandi, Sep 30 2011

Crossrefs

Cf. A104066, A168415, A188165.

Sequence in context: A267437 A267438 A102273 * A104066 A184394 A060160

Adjacent sequences: A195460 A195461 A195462 * A195464 A195465 A195466

Keyword

nonn,easy

Author

Brad Clardy, Sep 19 2011

Status

approved