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

Author

M. F. Hasler, Aug 29 2012

Keywords

• nonn

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).

Crossrefs

The numerator of the sum is given in A215990.

Programs

PARI

s=0;for(k=1,199,print1(valuation(denominator(s+=k!/2^k),2),","))

Formula

denominator( sum( k!/2^k, k=1..n )) = 2^a(n).

a(n)=0 <=> n is in A215974 <=> n+1 is in A215972.