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, 5455

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..19.

Example

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

Mathematica

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

Crossrefs

Cf. A120266, A119029, A120267.

Sequence in context: A017846 A179053 A218949 * A105181 A263361 A320020

Adjacent sequences: A129973 A129974 A129975 * A129977 A129978 A129979

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Jun 13 2007

Extensions

Edited by Stefan Steinerberger, Jul 22 2007

3 more terms from Ryan Propper, Jan 22 2008

Status

approved