A135723 -id:A135723 - cp's OEIS frontend

A005095 a(n) = n! + n.

1, 2, 4, 9, 28, 125, 726, 5047, 40328, 362889, 3628810, 39916811, 479001612, 6227020813, 87178291214, 1307674368015, 20922789888016, 355687428096017, 6402373705728018, 121645100408832019, 2432902008176640020, 51090942171709440021

Offset: 0

N. J. A. Sloane

Every infinite, increasing, integer arithmetic progression meets this sequence infinitely often. - John Abbott (abbott(AT)dima.unige.it), Mar 06 2003
Sum(A010051(k): A038507(n) < k <= a(n)) = 0. - Reinhard Zumkeller, Jul 10 2009
Largest k such that (k!-n!)/(k-n) is an integer. - Derek Orr, Apr 02 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 5.
Index entries for sequences related to factorial numbers

Cf. A135723.

Cf. A090786. - Reinhard Zumkeller, Jul 10 2009

[Factorial(n) + n: n in [0..20]]; // Vincenzo Librandi, Jun 08 2013

lst={};Do[AppendTo[lst, n!+n], {n, 3*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 20 2008 *)
Table[n! + n, {n, 0, 20}] (* Vincenzo Librandi, Jun 08 2013 *)

A005095(n):= n!+n$
makelist(A005095(n),n,0,30); /* Martin Ettl, Nov 03 2012 */

E.g.f.: x*exp(x) + 1/(1-x). - Len Smiley, Dec 05 2001
Row sums of triangle A135723. - Gary W. Adamson, Nov 25 2007
(n-1)*(n-3)*a(n) -n*(n^2-3*n+1)*a(n-1) +n*(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Oct 30 2015
a(n) +(-n-3)*a(n-1) +3*(n)*a(n-2) +(-3*n+5)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Oct 30 2015

A135724 Fibonacci numbers whose indices are prime Fibonacci numbers: a(n) = Fibonacci(A001605(n)).

Original entry on oeis.org

1, 2, 5, 233, 1779979416004714189, 2211236406303914545699412969744873993387956988653

Offset: 1

Artur Jasinski, Nov 26 2007

nonn

The only known prime numbers in this sequence are 2, 5 and 233.

The next term (a(6)) has 334 digits. - Harvey P. Dale, Apr 28 2023

Amiram Eldar, Table of n, a(n) for n = 1..7

Cf. A000045, A001605, A135723, A134787, A134788, A134789, A134790.

a = {}; b = {}; Do[If[PrimeQ[c = Fibonacci[n]], w = Fibonacci[Fibonacci[n]]; AppendTo[a, w]; AppendTo[b, n]], {n, 1, 31}]; a
Fibonacci[#]&/@Select[Fibonacci[Range[20]],PrimeQ] (* Harvey P. Dale, Apr 28 2023 *)

Corrected by Harvey P. Dale, Apr 28 2023

cp's OEIS Frontend

A005095 a(n) = n! + n.

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