A129976 Numbers k such that the numerator of Sum_{j=0..k} k^j/j! is a prime number.

1, 2, 3, 4, 5, 6, 8, 10, 14, 21, 33, 36, 56, 68, 94, 378, 1943, 2389, 2710, 5455, 6804

Offset: 1

Author

Alexander Adamchuk, Jun 13 2007

Keywords

• nonn
• hard
• more

Comments

The corresponding primes are A120266(a(n)) = {2, 5, 13, 103, 1097, 1223, ...}

a(22) > 10^4. - Michael S. Branicky, Apr 27 2025

Examples

			Sum_{j=0..4} 4^j/j! = 103/3. The numerator is a prime, hence 4 is in the sequence.
		

Crossrefs

Cf. A120266, A119029, A120267.

Programs

Mathematica

Do[ f=Numerator[Sum[n^k/k!,{k,0,n}]]; If[PrimeQ[f], Print[{n,f}]], {n, 1, 378}]

Extensions

Edited by Stefan Steinerberger, Jul 22 2007

a(17)-a(18) and a(20) from Ryan Propper, Jan 22 2008

a(19) and a(21) from Michael S. Branicky, Apr 26 2025