A215976 2-adic valuation of the denominator of sum( k!/2^k, k=1..n ).

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).

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: A072738 A165316 A362991 * A141058 A102706 A105673

Adjacent sequences: A215973 A215974 A215975 * A215977 A215978 A215979

Keyword

nonn

Author

M. F. Hasler, Aug 29 2012

Status

approved