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

Author

M. F. Hasler, Aug 29 2012

Keywords

• nonn
• more

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

sum = 0; Select[Range[0, 10^4], IntegerQ[sum += #!/2^#] &] + 1 (* Robert Price, Apr 04 2019 *)

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,","))

Formula

A215974(n)=A215972(n)-1 for all n. (A215974 is the same with another convention for the upper limit of the sum.)

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