A299998 Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)/2).

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

Offset: 1

Author

M. F. Hasler, Feb 27 2018

Keywords

• nonn
• cons

Comments

The binary expansion is the characteristic function A010054 of the triangular numbers A000217.

Examples

			1.641632560655153866293842770225429434226061537956739747804651622380144603733...
		

Crossrefs

Cf. A000217, A010054, A190405, A333797.

Programs

Mathematica

RealDigits[QPochhammer[1/4, 1/4]/QPochhammer[2, 1/4], 10, 100][[1]] (* Amiram Eldar, Aug 13 2020 *)

PARI

default(realprecision,200);suminf(k=0,2^(-k*(k+1)/2))

Formula

Equals 1 + A190405 (as a decimal number).

Equals Product{k>=1} (1 - 1/2^(2*k))/(1 - 1/2^(2*k-1)). - Amiram Eldar, Aug 13 2020