A346171 Decimal expansion of Sum_{k>=1} primepi(k)^2/k!.

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

Table of n, a(n) for n=1..100.

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

Cf. A000142, A000720, A346170.

Sequence in context: A179411 A103859 A253808 * A007400 A057696 A057697

Adjacent sequences: A346168 A346169 A346170 * A346172 A346173 A346174

Keyword

nonn,cons

Author

Amiram Eldar, Jul 08 2021

Status

approved