A258716 - OEIS

A258716

Decimal expansion of 3 + 2*Sum_{k>=0} 1/Product_{i=0..k} (2^(2^i) - 1).

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..80.

Gary W. Adamson and N. J. A. Sloane, Correspondence, May 1994, including Adamson's MSS "Algorithm for Generating nth Row of Pascal's Triangle, mod 2, from n", and "The Tower of Hanoi Wheel". Defines this number.

FORMULA

Equals 3 + A258715.

From Amiram Eldar, Feb 19 2024: (Start)

Equals 2 * A258714 + 3.

Equals 2/A215016. (End)

Equals 1 / (1 - 2*A014571). - Guido Vranken, Feb 18 2026

From Amiram Eldar, Aug 05 2026: (Start)

Equals Product_{k>=0} (1 + 2/(2^(2^k) - 1)).

Equals Product_{k>=1} exp(1/lcm(k, 2^(k-1))) = exp(Sum_{n>=1} 1/A014964(n)). (End)

EXAMPLE

5.7112854057096334466665254291814791046797658771989754...

MATHEMATICA