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Decimal expansion of Sum_{n>=1} A006218(n)*2^(-n).
8

%I #16 Jun 09 2024 22:01:28

%S 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,

%T 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,

%U 3,6,8,4,1,4,8,6,9,7,3,3,8,1,1,3,1,4,2

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

%F Equals 2 * A065442. - _Amiram Eldar_, Aug 01 2020

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

%t f[n_, m_] := Sum[Floor[n/k], {k, 1, m}]

%t t = Table[f[n, 100], {n, 1, 4000}] ;

%t N[Sum[t[[n]]/2^n, {n, 1, 4000}], 100]

%t RealDigits[%, 10] (* A211705 *)

%t RealDigits[%%, 2] (* A211706 *)

%o (PARI) k=1.; 2*suminf(n=1, k>>=1; k^n*(1+k)/(1-k)) \\ _Charles R Greathouse IV_, Jul 18 2021

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

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Apr 19 2012

%E a(31) onward corrected by _Sean A. Irvine_, Jun 09 2024