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A383903 Decimal expansion of Meissel Prime theta function at x = 2 : Sum_{p prime} 1/exp(2*p).

%I A383903 #26 Aug 14 2025 20:17:03
%S A383903 0,2,0,8,4,0,6,2,2,8,0,7,9,3,9,7,7,0,7,6,1,4,2,8,7,9,5,4,3,4,7,6,4,5,
%T A383903 3,5,8,8,8,7,2,8,1,6,0,4,6,1,4,5,6,8,0,0,5,8,1,8,4,9,2,6,5,4,3,8,2,4,
%U A383903 6,1,9,8,8,8,8,3,7,8,1,5,7,3,2,2,4,9,2,0,9,3,4,7,2,3,5,9,4,8,9,7,5,7,2,4,1,4,8,7,4,2,1
%N A383903 Decimal expansion of Meissel Prime theta function at x = 2 : Sum_{p prime} 1/exp(2*p).
%C A383903 Meissel Prime theta function is defined : Sum_{p prime} 1/exp(x*p).
%D A383903 Ernst Meissel, Bericht über die Provinzial-Gewerbe-Schule zu Iserlohn. Notiz No. 38 pp.1-17 (manuscript).
%H A383903 Peter Lindqvist and Jaak Peetre, <a href="https://oeis.org/A077761/a077761.pdf">On a number theoretic sum considered by Meissel : a historical observation</a>, Nieuw Archief voor Wiskunde (Serie 4) 1997 Vol. 15 (3) pp. 175-179 (see reprint p. 3).
%e A383903 0.02084062280793977076142879543476453588872816...
%p A383903 evalf[140](sum(1/exp(2*ithprime(i)), i=1..infinity));  # _Alois P. Heinz_, Aug 07 2025
%t A383903 sum = 0; Do[sum = sum + N[1/E^(2 Prime[n]), 110], {n, 1, 56}];
%t A383903 RealDigits[sum, 10, 105][[1]]
%o A383903 (PARI) sumpos(k = 1, exp(-2*prime(k))) \\ _Amiram Eldar_, Aug 08 2025
%Y A383903 Cf. A077761, A383901.
%K A383903 nonn,cons
%O A383903 0,2
%A A383903 _Artur Jasinski_, Aug 07 2025