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A346171
Decimal expansion of Sum_{k>=1} primepi(k)^2/k!.
1
1, 4, 2, 4, 4, 5, 3, 9, 4, 7, 5, 0, 4, 7, 9, 7, 2, 1, 8, 2, 4, 7, 3, 7, 5, 2, 3, 3, 6, 8, 1, 4, 7, 4, 1, 8, 0, 0, 4, 5, 6, 4, 5, 2, 9, 6, 4, 5, 9, 0, 7, 0, 5, 4, 1, 5, 0, 0, 3, 2, 6, 2, 9, 3, 6, 8, 2, 5, 2, 5, 4, 3, 0, 7, 7, 5, 0, 7, 1, 7, 0, 6, 9, 5, 9, 4, 7, 4, 3, 3, 1, 2, 6, 8, 4, 3, 4, 1, 1, 3
OFFSET
1,2
COMMENTS
This constant is irrational (Hančl and Tijdeman, 2010).
LINKS
Jaroslav Hančl and Robert Tijdeman, On the irrationality of factorial series II, Journal of Number Theory, Vol. 130, No. 3 (2010), pp. 595-607.
EXAMPLE
1.42445394750479721824737523368147418004564529645907...
MATHEMATICA
RealDigits[Sum[PrimePi[i]^2/i!, {i, 1, 100}], 10, 100][[1]]
PROG
(PARI) suminf(k=1, primepi(k)^2/k!) \\ Michel Marcus, Jul 09 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 08 2021
STATUS
approved