

A215976


2adic 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
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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).


LINKS

Table of n, a(n) for n=1..87.


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: A241533 A072738 A165316 * A141058 A102706 A105673
Adjacent sequences: A215973 A215974 A215975 * A215977 A215978 A215979


KEYWORD

nonn


AUTHOR

M. F. Hasler, Aug 29 2012


STATUS

approved



