login
A371135
Decimal expansion of Sum_{powerful k>=1} k / 2^k.
1
7, 9, 9, 0, 7, 3, 2, 1, 9, 8, 2, 3, 2, 7, 2, 3, 9, 9, 4, 4, 1, 0, 6, 4, 3, 2, 3, 2, 1, 0, 0, 5, 0, 6, 4, 5, 3, 1, 7, 2, 2, 2, 4, 6, 5, 3, 9, 8, 5, 2, 9, 3, 3, 3, 2, 9, 0, 2, 0, 9, 1, 2, 5, 8, 6, 8, 5, 9, 4, 6, 2, 8, 9, 9, 4, 7, 8, 6, 2, 6, 1, 1, 7, 8, 0, 3, 9, 2, 2, 4, 6, 6, 8, 9, 2, 2, 3, 7, 4, 3, 8, 5, 7, 8, 7, 1, 8, 5, 5, 0, 5, 9, 6, 1, 8, 8, 6, 2, 6, 2
OFFSET
0,1
COMMENTS
Chen and Ruzsa (1999) proved that this constant is irrational.
LINKS
Yong-Gao Chen and Imre Z. Ruzsa, On the irrationality of certain series, Periodica Mathematica Hungarica, Vol. 38, No. 1 (1999), pp. 31-37.
FORMULA
Equals Sum_{k>=1} A001694(k) / 2^A001694(k).
Equals Sum_{k>=1} k * A112526(k) / 2^k.
EXAMPLE
0.79907321982327239944106432321005064531722246539852...
MATHEMATICA
RealDigits[Sum[n/2^n, {n, Select[Range[1000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]}], 10, 120][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 12 2024
STATUS
approved