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URL: https://oeis.org/A215972

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A215972
Numbers k such that Sum_{j=1..k-1} j!/2^j is an integer.
9
1, 3, 6, 13, 15, 26, 30, 55, 61, 63, 3446, 108996, 3625183, 13951973, 28010902, 7165572248, 14335792540, 114636743487, 229264368710, 458534096495
OFFSET
1,2
LINKS
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
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