A211705 Decimal expansion of Sum_{n>=1} A006218(n)*2^(-n).

3, 2, 1, 3, 3, 9, 0, 3, 0, 4, 8, 3, 0, 5, 8, 3, 5, 2, 7, 5, 6, 6, 6, 0, 3, 0, 4, 6, 3, 8, 1, 8, 4, 9, 1, 6, 0, 9, 6, 1, 1, 5, 9, 3, 4, 3, 0, 1, 1, 5, 1, 2, 8, 7, 1, 5, 5, 6, 1, 5, 9, 1, 0, 7, 3, 8, 2, 8, 3, 6, 8, 4, 1, 4, 8, 6, 9, 7, 3, 3, 8, 1, 1, 3, 1, 4, 2

Offset: 1

Author

Clark Kimberling, Apr 19 2012

Keywords

• nonn
• cons

Examples

			Sum_{n>=1} A006218(n)*2^(-n) = 1/2 + 3/4 + 5/8 + 8/16 + 10/32 + 14/64 + ... = 3.213390304830583527566603046381849...
		

Crossrefs

Cf. A006218, A065442, A211701, A211706 (binary).

Programs

Mathematica

f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]
t = Table[f[n, 100], {n, 1, 4000}] ;
N[Sum[t[[n]]/2^n, {n, 1, 4000}], 100]
RealDigits[%, 10]  (* A211705 *)
RealDigits[%%, 2]  (* A211706 *)

PARI

k=1.; 2*suminf(n=1, k>>=1; k^n*(1+k)/(1-k)) \\ Charles R Greathouse IV, Jul 18 2021

Formula

Equals 2 * A065442. - Amiram Eldar, Aug 01 2020

Extensions

a(31) onward corrected by Sean A. Irvine, Jun 09 2024