A147615 a(n) = 13 + Sum_{j=4..n+3} j!.

13, 37, 157, 877, 5917, 46237, 409117, 4037917, 43954717, 522956317, 6749977117, 93928268317, 1401602636317, 22324392524317, 378011820620317, 6780385526348317, 128425485935180317, 2561327494111820317, 53652269665821260317, 1177652997443428940317

Offset: 0

Author

Ricky Pollack (rickypollack(AT)gmail.com), Apr 30 2009

Keywords

• nonn

Comments

Are there infinitely many terms in the intersection of this sequence and A036570?

Answer from Don Reble, Mar 25 2016: No, after the ninth term, all terms are multiples of 13.

Examples

			a(0) = 13, a(1) = 13 + 4!, a(2) = 13 + 4! + 5!, ....
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A003422, A036570.

Programs

Magma

[n eq 0 select 13 else 13 + (&+[Factorial(j+4): j in [0..n-1]]): n in [0..30]]; // G. C. Greubel, Oct 24 2022

Mathematica

A147615[n_]:= 13 +Sum[j!, {j,4,n+3}]; Table[A147615[n], {n,0,30}] (* G. C. Greubel, Oct 24 2022 *)

SageMath

def A147615(n): return 13 + sum(factorial(j+4) for j in range(n))
[A147615(n) for n in range(30)] # G. C. Greubel, Oct 24 2022

Formula

a(n) = 13 + !(n+4) - !4 = 13 + A003422(n+4) - A003422(4). - G. C. Greubel, Oct 24 2022