A074824 -id:A074824 - cp's OEIS frontend

A117591 a(n) = 2^n + Fibonacci(n).

1, 3, 5, 10, 19, 37, 72, 141, 277, 546, 1079, 2137, 4240, 8425, 16761, 33378, 66523, 132669, 264728, 528469, 1055341, 2108098, 4212015, 8417265, 16823584, 33629457, 67230257, 134414146, 268753267, 537385141, 1074573864, 2148829917

Offset: 0

Franklin T. Adams-Watters, Apr 04 2006

a(3n) is even if n>0. - Robert G. Wilson v, Sep 06 2002

3 divides a(8n+1) and a(8n-1). - Enrique Pérez Herrero, Dec 29 2010

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Cf. A000045, A000079, A001611, A074824, A099036, A212262.

a117591 n = a117591_list !! n
a117591_list = zipWith (+) a000079_list a000045_list
-- Reinhard Zumkeller, Aug 15 2013

[2^n+Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Nov 02 2014

Table[f=Fibonacci[n];2^n+f,{n,1,40,1}] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
CoefficientList[Series[(1-3x^2)/((1-x-x^2)(1-2x)), {x,0,35}], x] (* Vincenzo Librandi, Nov 02 2014 *)

a(n)=2^n + fibonacci(n) \\ Charles R Greathouse IV, Oct 07 2016

[2^n +fibonacci(n) for n in (0..40)] # G. C. Greubel, Jul 05 2021

G.f. (1-3*x^2)/((1-x-x^2)*(1-2*x)).

a(n) = A000079(n+1) - A099036(n) = A099036(n) + 2 * A000045(n). - Reinhard Zumkeller, Aug 15 2013

A074716 Numbers k such that 2^k - F(k) is prime, where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

2, 4, 14, 23, 55, 80, 104, 286, 335, 383, 809, 1664, 2096, 2624, 4262, 13544, 14249, 19886, 35500, 40591, 42920, 50839, 56696, 114505

Offset: 1

Benoit Cloitre, Sep 04 2002

1664 and above are pseudoprimes only. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Dec 26 2004

1664, 2096, 2624 and 4262 correspond to certified primes. (Primo 2.2.0 beta) - Ryan Propper, Aug 29 2005

Cf. A000045, A074824.

Do[ If[ PrimeQ[ 2^n - Fibonacci[n]], Print[n]], {n, 1, 5000}]

Edited by Robert G. Wilson v, Sep 06 2002
a(16)-a(20) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Dec 18 2004
a(21)-a(23) from Michael S. Branicky, May 19 2023
a(24) from Michael S. Branicky, Aug 03 2024

A292614 Numbers k such that 2^k - Lucas(k) is prime.

Original entry on oeis.org

14, 19, 25, 41, 46, 65, 136, 145, 185, 193, 290, 406, 481, 641, 761, 3481, 4873, 5360, 6682, 13579, 34120, 35384, 43070, 46744, 96014, 212521

Offset: 1

Amiram Eldar, Sep 20 2017

a(26) > 139000. - Giovanni Resta, Sep 21 2017

Cf. A000032, A074716, A074824, A275368.

Select[Range[0, 6000], PrimeQ[2^# - LucasL[#]] &]

a(24)-a(25) from Giovanni Resta, Sep 21 2017

a(26) from Michael S. Branicky, Apr 25 2025

cp's OEIS Frontend

A117591 a(n) = 2^n + Fibonacci(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

PARI

Sage

Formula

A074716 Numbers k such that 2^k - F(k) is prime, where F(n) is the n-th Fibonacci number.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A292614 Numbers k such that 2^k - Lucas(k) is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions