A365307 Decimal expansion of 1/(2*e-5).

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

Offset

1,1

Comments

The continued fraction expansion is A081750 with initial term 5 omitted.

Links

Table of n, a(n) for n=1..90.

Formula

Equals 2 + 1/(3 + 2/(4 + 3/(5 + 4/(6 + 5/( ... /(n+1 + n/(n+2 + ... ))))))).

From Peter Bala, Oct 23 2023: (Start)

Define s(n) = Sum_{k = 3..n} 1/k!. Then 1/(2*e - 5) = 3 - (1/2)*Sum_{n >= 3 } 1/( (n+1)!*s(n)*s(n+1) ) is a rapidly converging series of rationals. Cf. A073333 and A194807.

Equivalently, 1/(2*e - 5) = 3 - (1/2)*(3!/(1*5) + 4!/(5*26) + 5!/(26*157) + 6!/(157*1100) + ...), where [1, 5, 26, 157, 1100, ... ] is A185108. (End)

Example

2.2906166927853624221...

Mathematica

A365307 = RealDigits[N[1/(2*E-5), #+1]][[1]][[1;; -2]]&;

Prog

(PARI) 1/(2*exp(1)-5).

Crossrefs

Cf. A001113, A194807, A019762, A113011, A081750, A073333, A185108.

Sequence in context: A326939 A341303 A011148 * A351400 A176020 A048650

Adjacent sequences: A365304 A365305 A365306 * A365308 A365309 A365310

Keyword

nonn,cons

Author

Rok Cestnik, Aug 31 2023

Status

approved