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

Author

Ryan Propper, Aug 01 2005

Keywords

• nonn
• hard
• more

Comments

Terms through 807 correspond to certified primes.

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

Examples

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

Crossrefs

Cf. A061354.

Programs

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 *)

Extensions

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