|
|
A343617
|
|
Decimal expansion of P_{3,2}(7) = Sum 1/p^7 over primes == 2 (mod 3).
|
|
1
|
|
|
0, 0, 7, 8, 2, 5, 3, 5, 4, 1, 1, 3, 0, 5, 0, 4, 9, 2, 8, 7, 4, 2, 5, 1, 7, 0, 1, 6, 7, 0, 7, 5, 5, 9, 2, 0, 6, 0, 3, 3, 0, 7, 9, 3, 0, 9, 7, 5, 1, 3, 2, 4, 4, 3, 3, 1, 4, 6, 8, 0, 4, 8, 8, 3, 3, 9, 4, 0, 3, 5, 4, 3, 7, 0, 6, 3, 8, 0, 9, 2, 1, 8, 4, 3, 5, 7, 0, 1, 1, 0, 5, 8, 6, 5, 3, 8, 3, 8, 6, 4, 5, 6, 2, 9, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The prime zeta modulo function P_{m,r}(s) = Sum_{primes p == r (mod m)} 1/p^s generalizes the prime zeta function P(s) = Sum_{primes p} 1/p^s.
|
|
LINKS
|
|
|
FORMULA
|
P_{3,2}(7) = Sum_{p in A003627} 1/p^7 = P(7) - 1/3^7 - P_{3,1}(7).
|
|
EXAMPLE
|
0.0078253541130504928742517016707559206033079309751324433146804883394...
|
|
PROG
|
(PARI) A343617_upto(N=100)={localprec(N+5); digits((PrimeZeta32(7)+1)\.1^N)[^1]} \\ see A343612 for the function PrimeZeta32
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|