A269992 Decimal expansion of Sum_{n>=1} 2^(1-n)/L(n), where L = A000032 (Lucas numbers).

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

Offset: 1

Author

Clark Kimberling, Mar 12 2016

Keywords

• nonn
• cons
• easy

Examples

			1.2552211343298486031402667274403360...
		

Crossrefs

Cf. A000032, A084057, A087131, A269991.

Programs

Mathematica

x = N[Sum[2^(1 - n)/LucasL[n], {n, 1, 500}], 100]
RealDigits[x][[1]]

PARI

L(n) = real((2 + quadgen(5)) * quadgen(5)^n); \\ A000032
suminf(n=1, 2^(1-n)/L(n)) \\ Michel Marcus, Nov 17 2020

Formula

Equals Sum_{n>=1} 1/A084057(n) = 2 * Sum_{n>=1} 1/A087131(n). - Amiram Eldar, Feb 01 2021