The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A371136

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A371136

Decimal expansion of Sum_{k>=1} 1/Fibonacci(k!).
(history; published version)

#7 by Michel Marcus at Tue Mar 12 02:47:20 EDT 2024

STATUS

reviewed

approved

#6 by Joerg Arndt at Tue Mar 12 02:33:48 EDT 2024

STATUS

proposed

reviewed

#5 by Amiram Eldar at Tue Mar 12 02:11:39 EDT 2024

STATUS

editing

proposed

#4 by Amiram Eldar at Tue Mar 12 02:11:14 EDT 2024

FORMULA

Equals Sum_{k>=1} 1/A063374(k).

#3 by Amiram Eldar at Tue Mar 12 01:56:32 EDT 2024

NAME

allocated for Amiram EldarDecimal expansion of Sum_{k>=1} 1/Fibonacci(k!).

DATA

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

OFFSET

1,1

COMMENTS

Nyblom (2000) proved that this constant is transcendental.

LINKS

M. A. Nyblom, <a href="https://doi.org/10.1216/rmjm/1021477261">A theorem on transcendence of infinite series</a>, The Rocky Mountain Journal of Mathematics, Vol. 30, No. 3 (2000), pp. 1111-1120; <a href="https://www.jstor.org/stable/44238526">alternative link</a>.

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

EXAMPLE

2.12502156659765355417529349235237991793625797423002...

MATHEMATICA

RealDigits[Sum[1/Fibonacci[k!], {k, 1, 10}], 10, 120][[1]]

PROG

(PARI) suminf(k = 1, 1/fibonacci(k!))

CROSSREFS

Cf. A000045, A000142, A063374, A343202, A371137.

KEYWORD

allocated

nonn,cons

AUTHOR

Amiram Eldar, Mar 12 2024

STATUS

approved

editing

#2 by Amiram Eldar at Tue Mar 12 01:54:31 EDT 2024

KEYWORD

allocating

allocated

#1 by Amiram Eldar at Tue Mar 12 01:54:31 EDT 2024

NAME

allocated for Amiram Eldar

KEYWORD

allocating

STATUS

approved