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Decimal expansion of 90/781.
0

%I #16 May 17 2024 02:54:28

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

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

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

%N Decimal expansion of 90/781.

%H J. M. Borwein and P. B. Borwein, <a href="https://doi.org/10.2307/2324993">Strange Series and High Precision Fraud</a>, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

%H <a href="/index/Rec#order_70">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F Equals Sum_{j >= 1} f(j)/2^j, where f(j) = Sum_{k >= 0, (k+1)-th digit from the right of 2^j is odd} A007598(k). See Example 5.1 (c) in Borwein and Borwein (1992), pp. 638-639.

%e 0.11523687580025608194622279129321382842509603072983354673...

%t First[RealDigits[90/781, 10, 100]]

%Y Cf. A000079, A007598, A021785.

%K nonn,cons,easy

%O 0,3

%A _Paolo Xausa_, May 13 2024