A048649 Decimal expansion of Sum_{m>=0} 1/(2^2^m - 1).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			1.40393682788217832057620607413720935453...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for transcendental numbers.

Crossrefs

A048649 + A051158 = 2.

Cf. A007814, A048164, A048650.

Programs

Mathematica

NSum[1/(2^2^m - 1), {m, 0, Infinity}, WorkingPrecision -> 99] // RealDigits // First (* Jean-François Alcover, Feb 12 2013 *)

PARI

{ default(realprecision, 20080); x=suminf(m=0, 1/(2^2^m - 1)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b048649.txt", n, " ", d)); } \\ Harry J. Smith, May 07 2009

Formula

Equals 1 + Sum_{n>=1} A007814(n)/2^n = 4/3 + Sum_{n>=1} A007814(n)/4^n = 7/5 + Sum_{n>=1} A007814(n)/16^n. - Amiram Eldar, Nov 06 2020

Extensions

Deleted old PARI program. - Harry J. Smith, May 20 2009