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A365307 Decimal expansion of 1/(2*e-5). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The continued fraction expansion is A081750 with initial term 5 omitted.
LINKS
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
Sequence in context: A326939 A341303 A011148 * A351400 A176020 A048650
KEYWORD
nonn,cons
AUTHOR
Rok Cestnik, Aug 31 2023
STATUS
approved

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)