A060388 Decimal expansion of alpha(2) = Sum_{i>0} prime(i)*2^(-i^2).

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

Offset

1,3

Comments

prime(n) = floor(2^(n^2)*alpha(2))-2^(2*n-1)*floor(2^((n-1)^2)*alpha(2)). For n = 6 we have prime(6) = floor(2^36*alpha(2))-2^11*floor(2^25*alpha(2)) = 82282829837-2048*40177163 = 13.

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1979, page 345.

Links

Table of n, a(n) for n=1..105.

Example

alpha(2) = 1.19737276453818886171347795420537819781902821399037219013\
077245140303647694034267909212754914431410431122998171762351103482006\
076264716653454638...

Prog

(PARI) suminf(i=1, prime(i)/2^(i^2)) \\ Michel Marcus, May 25 2018

Crossrefs

Sequence in context: A033873 A260880 A135449 * A081821 A164102 A105532

Adjacent sequences: A060385 A060386 A060387 * A060389 A060390 A060391

Keyword

nonn,cons

Author

Vladeta Jovovic, Apr 03 2001

Status

approved