A215974 Numbers n such that Sum_{k=1..n} k!/2^k is an integer.

0, 2, 5, 12, 14, 25, 29, 54, 60, 62, 3445, 108995, 3625182, 13951972, 28010901, 7165572247, 14335792539, 114636743486, 229264368709, 458534096494

Offset

1,2

Comments

This sequence lists the indices n for which A215976(n)=0 (power of 2 in denominator) and for which A215990 (numerator of the sum) may be even.

Links

Table of n, a(n) for n=1..20.

B. M. M. de Weger, Sums with factorials, NMBRTHRY list, Aug 28 2012

Formula

A215974(n) = A215972(n)-1 for all n. (The two sequences differ only in the use of the upper limit. The present convention seems more natural, the other one was used in the post on the NmbrThry list.)

Example

a(1)=0 is in the sequence because sum(..., 1 <= k <= 0)=0 (empty sum) is an integer.
1 is not in the sequence because 1!/2^1 = 1/2 is not an integer.
a(2)=2 is in the sequence because 1!/2^1 + 2!/2^2 = 1 is an integer.

Mathematica

sum = 0; Select[Range[0, 10^4], IntegerQ[sum += #!/2^#] &] (* Robert Price, Apr 04 2019 *)

Prog

(PARI) is_A215974(n)=denominator(sum(k=1, n, k!/2^k))==1
(PARI) s=0; for(k=1, 9e9, denominator(s+=k!/2^k)==1&print1(k, ", "))

Crossrefs

Cf. A215972, A216056.

Sequence in context: A286160 A286163 A286240 * A192524 A287553 A102718

Adjacent sequences: A215971 A215972 A215973 * A215975 A215976 A215977

Keyword

nonn,more

Author

M. F. Hasler, Aug 29 2012

Extensions

Terms through a(20) from Aart Blokhuis and Benne de Weger, Aug 30 2012, who thank Jan Willem Knopper for efficient programming. - N. J. A. Sloane, Aug 30 2012

Status

approved