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A064890
Decimal expansion of the sum of reciprocals of A051451, which includes 1 and values of lcm(1,...,x), where x is a prime power (A000961).
2
1, 7, 7, 0, 6, 7, 5, 2, 4, 4, 3, 2, 5, 5, 8, 0, 2, 2, 7, 9, 1, 9, 7, 9, 6, 0, 0, 7, 6, 4, 2, 6, 6, 0, 8, 0, 2, 2, 3, 3, 1, 8, 3, 7, 6, 7, 2, 7, 2, 8, 3, 3, 5, 2, 0, 5, 2, 2, 4, 5, 8, 9, 6, 4, 4, 1, 2, 2, 2, 0, 3, 3, 8, 1, 0, 2, 2, 9, 6, 1, 1, 0, 5, 6, 5, 0, 7, 0, 5, 7, 7, 5, 7, 0, 8, 0, 9, 3, 4, 0, 3, 3, 3, 0, 2
OFFSET
1,2
LINKS
Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 37.
EXAMPLE
c = 1.7706752443255802279197960076426608022331837672728335205224589644122203381...
c = 1 + (1/2) + (1/6) + (1/12) + (1/60) + (1/420) + ... = 743/420 + ... = 1.7690 + ... = 1.7706752... Compare with A064859, an analogous constant obtained from A003418, where the constant is larger than c: 1.7877805 > 1.7706752. Repeated occurrences of LCM values in A003418 is responsible for the 1.78778... - 1.77067... = 0.0171... excess.
MATHEMATICA
f[n_] := LCM @@ Range@ n; RealDigits[ Plus @@ (1/Union@ Array[f, 251]), 10, 111][[1]] (* Robert G. Wilson v, Jul 11 2011 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Labos Elemer, Oct 11 2001
STATUS
approved