A346170 Decimal expansion of Sum_{k>=1} 2^primepi(k)/k!.

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

Offset

1,1

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

2.91473192010176315429638470222867569008572970452727...

Mathematica

RealDigits[Sum[2^PrimePi[i]/i!, {i, 1, 100}], 10, 100][[1]]

Prog

(PARI) suminf(k=1, 2^primepi(k)/k!) \\ Michel Marcus, Jul 09 2021

Crossrefs

Cf. A000142, A000720, A048656, A346171.

Sequence in context: A173995 A272868 A074950 * A113211 A244807 A021347

Adjacent sequences: A346167 A346168 A346169 * A346171 A346172 A346173

Keyword

nonn,cons

Author

Amiram Eldar, Jul 08 2021

Status

approved