A383901 Decimal expansion of Meissel Prime theta function at 1 : Sum_{p prime} 1/exp(p).

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

Offset: 0

Author

Artur Jasinski, Aug 07 2025

Keywords

• nonn
• cons

Comments

Meissel Prime theta function is defined : Sum_{p prime} 1/exp(x*p).

Examples

			0.192791189704395145042150125418556376792365...
		

References

• Ernst Meissel, Bericht über die Provinzial-Gewerbe-Schule zu Iserlohn. Notiz No. 38 pp. 1-17 (manuscript).

Links

• Peter Lindqvist and Jaak Peetre, On a number theoretic sum considered by Meissel : a historical observation, Nieuw Archief voor Wiskunde (Serie 4) 1997 Vol. 15 (3) pp. 175-179 (see reprint p. 3).

Crossrefs

Cf. A077761, A383903.

Programs

Maple

evalf[140](sum(1/exp(ithprime(i)), i=1..infinity));  # Alois P. Heinz, Aug 07 2025

Mathematica

sum = 0; Do[sum = sum + N[1/E^(Prime[n]), 110], {n, 1, 56}];
RealDigits[sum, 10, 105][[1]]

PARI

sumpos(k = 1, exp(-prime(k))) \\ Amiram Eldar, Aug 08 2025