A346173 Decimal expansion of Sum_{k>=1} prime(k)/2^prime(k).

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

Offset: 1

Author

Amiram Eldar, Jul 08 2021

Keywords

• nonn
• cons

Comments

This constant is irrational (Hančl and Tijdeman, 2004).

Links

• Jaroslav Hančl and Robert Tijdeman, On the irrationality of Cantor series, Journal für die reine und angewandte Mathematik, Vol. 2004, No. 571 (2004), pp. 145-158.

Crossrefs

Cf. A034785, A098990, A100127.

Programs

Mathematica

RealDigits[Sum[Prime[n]/2^Prime[n], {n, 1, 100}], 10, 100][[1]]

PARI

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

Formula

1.09306425770250716540258595269676368295547596540121...