A215016 Decimal expansion of the product of 1 - 1/2^2^n over all n >= 0.

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

Offset: 0

Author

Charles R Greathouse IV, Jul 31 2012

Keywords

• nonn
• cons

Comments

Can be used to efficiently compute A014571: A014571 = 1/2 - (1/4) * A215016.

Examples

			0.35018386543956960886655452696617886764208650217692176970648233860482563...
		

Links

• Joerg Arndt, Matters Computational (The Fxtbook), p.727 (rel. 38.1-5).
• R. Schroeppel and R. W. Gosper, HACKMEM #122 (1972).

Crossrefs

Cf. A001146, A014571, A106400, A258714, A258716.

Programs

Mathematica

RealDigits[NProduct[1 - 1/2^2^n, {n, 0, Infinity}, WorkingPrecision -> 120]][[1]] (* Alonso del Arte, Jul 31 2012 *)

PARI

prodinf(n=0,1-1.>>2^n)

Formula

Equals Sum_{n>=0} A106400(n)/2^n. - Robert FERREOL, Jan 10 2022

From Amiram Eldar, Feb 19 2024: (Start)

Equals Product_{n>=0} (1 - 1/A001146(n)).

Equals 2/A258716.

Equals 1/(3/2 + A258714). (End)