A109621 Numbers n such that the numerator of Sum_{k=0..n} 1/k!, in reduced form, is prime.

1, 2, 5, 9, 24, 32, 321, 343, 352, 511, 685, 807, 966, 1079, 1274, 1381, 2016, 3226, 8130

Offset

1,2

Comments

Terms through 807 correspond to certified primes.

If it exists, a(20) > 14304. - J.W.L. (Jan) Eerland, Sep 13 2022

Links

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

Example

Sum_{k=0..9} 1/k! = 98641/36288 and 98641 is prime, so 9 is in the sequence.

Mathematica

s = 0; Do[s += 1/n!; k = Numerator[s]; If[PrimeQ[k], Print[n]], {n, 0, 3300}]
Flatten[Position[Accumulate[1/Range[0, 3230]!], _?(PrimeQ[ Numerator[ #]]&)]] -1 (* Harvey P. Dale, Sep 25 2019 *)
n=0; Monitor[Parallelize[While[True, If[PrimeQ[Numerator[Sum[1/Factorial[k], {k, 0, n}]]], Print[n]]; n++]; n], n] (* J.W.L. (Jan) Eerland, Sep 13 2022 *)

Crossrefs

Cf. A061354.

Sequence in context: A192477 A288109 A047044 * A075200 A075198 A294633

Adjacent sequences: A109618 A109619 A109620 * A109622 A109623 A109624

Keyword

nonn,hard,more

Author

Ryan Propper, Aug 01 2005

Extensions

a(19) from J.W.L. (Jan) Eerland, Sep 13 2022

Status

approved