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A064859
Decimal expansion of sum of reciprocals of lcm(1..n) = A003418(n).
11
1, 7, 8, 7, 7, 8, 0, 4, 5, 6, 1, 7, 2, 4, 6, 6, 5, 4, 6, 0, 6, 4, 9, 3, 4, 3, 2, 6, 0, 2, 5, 6, 6, 2, 7, 9, 4, 5, 9, 3, 9, 6, 1, 7, 4, 7, 2, 9, 6, 9, 6, 0, 8, 3, 7, 2, 5, 3, 0, 2, 6, 9, 9, 2, 9, 2, 2, 8, 9, 0, 2, 3, 5, 0, 8, 2, 2, 3, 2, 6, 1, 5, 5, 2, 8, 3, 3, 6, 8, 7, 8, 0, 8, 5, 6, 9, 7, 9, 7, 9, 9, 4, 6, 9, 5
OFFSET
1,2
COMMENTS
This constant is irrational (Erdős and Graham, 1980). - Amiram Eldar, Apr 13 2020
LINKS
Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980. See p. 65.
Martin Griffiths and Des MacHale, 99.04 Another irrational number, The Mathematical Gazette, Vol. 99, No. 544 (2015), pp. 130-133.
Michael Penn, An irrational sum, YouTube video, 2022.
FORMULA
Equals Sum_{j>=1} 1/lcm(1..j).
EXAMPLE
1.7877804561724665460649343260256627945939617472969608372530269929228902350...
MATHEMATICA
f[n_] := LCM @@ Range@ n; RealDigits[Plus @@ (1/Array[f, 255]), 10, 111][[1]] (* Robert G. Wilson v, Jul 11 2011 *)
PROG
(PARI) suminf(k=1, 1/lcm(vector(k, j, j))) \\ Michel Marcus, Mar 11 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Labos Elemer, Oct 08 2001
STATUS
approved