A121472 - OEIS

A121472

A devil's staircase constant: decimal expansion of the sums involving powers of 2 and Beatty sequences given by: c = Sum_{n>=1} 1/2^[log_2(e^n)] = Sum_{n>=1} [log(2^n)]/2^n.

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

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OFFSET

0,1

COMMENTS

The continued fraction (A121473) of this constant has large partial quotients: c = [0; 1, 6, 146, 8, 37783544111994270385152, ...]. See the MathWorld link for more information regarding devil's staircase constants.

LINKS

Table of n, a(n) for n=0..103.

Eric Weisstein's World of Mathematics, Devil's Staircase

FORMULA

c = Sum_{n>=1} 1/2^[n/log(2)] = Sum_{n>=1} [n*log(2)]/2^n, where [z]=floor(z).

EXAMPLE

c=0.85728238310340617751190330850973399759098831209314692225782429246...

PROG

(PARI) a(n)=local(t=log(2), x=sum(m=1, 10*(n+1), 1/2^floor(m/t))); floor(10^n*x)%10

(PARI) a(n)=local(t=log(2), x=sum(m=1, 10*(n+1), floor(m*t)/2^m)); floor(10^n*x)%10

CROSSREFS

Cf. A121473 (continued fraction), A121474 (dual constant), A121475.