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A215974
Numbers n such that Sum_{k=1..n} k!/2^k is an integer.
5
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
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
Sequence in context: A286160 A286163 A286240 * A192524 A287553 A102718
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