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

Author

Brad Clardy, Sep 19 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A104066, A168415, A188165.

Programs

Magma

[4^(n+1) + 7: n in [0..30]]; // Vincenzo Librandi, Sep 30 2011

Mathematica

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

PARI

a(n)=4^(n+1)+7 \\ Charles R Greathouse IV, Sep 19 2011

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