A328495 Decimal expansion of Sum_{k>=0} (-1)^k*L(k)/k!, where L(k) is the k-th Lucas number (A000032).

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

Offset: 1

Author

Amiram Eldar, Oct 22 2019

Keywords

• nonn
• cons

Examples

			2.053565111476510960344914661146965309320258644945918...
		

References

• Thomas Koshy, Fibonacci and Lucas Numbers with Applications, Volume 1, 2nd edition, Wiley, 2017, chapter 13.8, pp. 248-250.

Crossrefs

Cf. A000032, A001113, A001622, A099935, A139341, A139342, A328344, A249455.

Programs

Maple

Digits := 100: 2*exp(-1/2)*cosh(sqrt(5)/2)*10^86:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Oct 22 2019

Mathematica

RealDigits[Exp[-GoldenRatio] + Exp[GoldenRatio - 1], 10, 100][[1]]

Formula

Equals exp(-phi) + exp(phi-1), where phi is the golden ratio (A001622).

Equals 2*exp(-1/2)*cosh(sqrt(5)/2) = A249455*cosh(phi - 1/2). - Peter Luschny, Oct 22 2019

Equals A328344 / e. - Amiram Eldar, Feb 06 2022