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A215976
2-adic valuation of the denominator of sum( k!/2^k, k=1..n ).
2
1, 0, 2, 2, 0, 2, 3, 3, 3, 3, 2, 0, 3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 0, 3, 4, 4, 0, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 2, 4, 0, 5, 5, 5, 5, 4, 0, 5, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
OFFSET
1,3
COMMENTS
By construction, this denominator is always a power of 2, the present sequence specifies which power. The sum is an integer iff a(n)=0, the corresponding n are listed in A215974 (= A215972 - 1).
FORMULA
denominator( sum( k!/2^k, k=1..n )) = 2^a(n).
a(n)=0 <=> n is in A215974 <=> n+1 is in A215972.
PROG
(PARI) s=0; for(k=1, 199, print1(valuation(denominator(s+=k!/2^k), 2), ", "))
CROSSREFS
The numerator of the sum is given in A215990.
Sequence in context: A072738 A165316 A362991 * A141058 A102706 A105673
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 29 2012
STATUS
approved