A372610 -id:A372610 - cp's OEIS frontend

A372766 Decimal expansion of Sum_{k >= 1} floor(k*log_10(2))/2^k.

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

Offset: 0

Paolo Xausa, May 12 2024

			0.14271749755620723362658846529824142150133752640380518206878...

Paolo Xausa, Table of n, a(n) for n = 0..10000
J. M. Borwein and P. B. Borwein, Strange Series and High Precision Fraud, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

Cf. A007524, A372610, A372767.

First[RealDigits[Sum[Floor[k*Log10[2]]/2^k, {k, 350}], 10, 100]]

Approximately 146/1023, correct to 30 digits: see Example 4.1 (d) in Borwein and Borwein (1992), p. 633.

A372767 Decimal expansion of Sum_{k >= 1} floor(k*zeta(3))/2^k.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, May 12 2024

			2.0645161290322580645161290322596931321914240243724629234896...

Paolo Xausa, Table of n, a(n) for n = 1..10000
J. M. Borwein and P. B. Borwein, Strange Series and High Precision Fraud, The American Mathematical Monthly, Vol. 99, No. 7 (1992), pp. 622-640.

Cf. A000079, A002117, A059537, A372610, A372766.

First[RealDigits[Sum[Floor[k*Zeta[3]]/2^k, {k, 350}], 10, 100]]

Equals Sum_{k >= 1} A059537(k)/A000079(k).

Approximately 64/31, correct to 30 digits: see Example 4.1 in Borwein and Borwein (1992), p. 634.

cp's OEIS Frontend

A372766 Decimal expansion of Sum_{k >= 1} floor(k*log_10(2))/2^k.

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