A109621 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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