login
A122153
Decimal expansion of Parity Prime Constant: Sum_{k>=1} (-1)^(k+1) * 1/(2^prime(k)).
4
1, 4, 8, 8, 0, 9, 5, 5, 0, 7, 8, 8, 7, 7, 6, 2, 2, 4, 9, 6, 9, 5, 6, 8, 4, 6, 7, 8, 6, 6, 7, 9, 6, 5, 3, 1, 9, 8, 2, 2, 2, 4, 1, 3, 2, 8, 0, 8, 2, 1, 7, 0, 6, 7, 3, 7, 1, 7, 7, 0, 0, 0, 0, 5, 6, 3, 3, 1, 3, 9, 1, 2, 6, 2, 2, 3, 3, 3, 7, 4, 5, 1, 8, 4, 9, 4, 5, 1, 4, 3, 7, 7, 8, 8, 8, 0, 8, 5, 2
OFFSET
0,2
COMMENTS
Binary expansion is given in A071986(n) = pi(n) mod 2.
FORMULA
Equals Sum_{k>=1} (-1)^(k+1) * 1/(2^prime(k)).
Equals lim_{n->infinity} A122150(n)/A034765(n).
EXAMPLE
0.148809550788776224969568467866796531982224132808217067371770000563313912...
MATHEMATICA
RealDigits[Sum[(-1)^(k+1)*1/2^Prime[k], {k, 1, 1000}], 10, 100]
PROG
(PARI) suminf(k=1, (-1)^(k+1) * 1/2^prime(k)) \\ Michel Marcus, Mar 20 2019
KEYWORD
nonn,cons
AUTHOR
Alexander Adamchuk, Aug 22 2006
EXTENSIONS
Offset corrected by R. J. Mathar, Feb 05 2009
Edited by Michel Marcus, Mar 20 2019
STATUS
approved