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
Examples
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.
Links
- B. M. M. de Weger, Sums with factorials, NMBRTHRY list, Aug 28 2012
Programs
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Mathematica
sum = 0; Select[Range[0, 10^4], IntegerQ[sum += #!/2^#] &] (* Robert Price, Apr 04 2019 *)
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PARI
is_A215974(n)=denominator(sum(k=1,n,k!/2^k))==1
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PARI
s=0;for(k=1,9e9,denominator(s+=k!/2^k)==1&print1(k,","))
Formula
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
Comments