A215972 Numbers k such that Sum_{j=1..k-1} j!/2^j is an integer.

1, 3, 6, 13, 15, 26, 30, 55, 61, 63, 3446, 108996, 3625183, 13951973, 28010902, 7165572248, 14335792540, 114636743487, 229264368710, 458534096495

Offset

1,2

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. (A215974 is the same with another convention for the upper limit of the sum.)

Example

a(1)=1 is in the sequence because sum(..., 0<k<1)=0 (empty sum) is an integer.
2 is not in the sequence because 1!/2^1 = 1/2 is not an integer.
a(2)=3 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^#] &] + 1 (* Robert Price, Apr 04 2019 *)

Prog

(PARI) is_A215972(n)=denominator(sum(k=1, n-1, k!/2^k))==1
(PARI) s=0; for(k=1, 9e9, denominator(s+=k!/2^k)==1&print1(k+1, ", "))

Crossrefs

Cf. A215974, A216056, A216042, A216043, A216044, A216045.

Sequence in context: A257276 A248043 A189420 * A341249 A145604 A053569

Adjacent sequences: A215969 A215970 A215971 * A215973 A215974 A215975

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