OFFSET
-8,2
LINKS
Robert G. Wilson v, Table of n, a(n) for n = -8..10000
Carl Pomerance, Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. Iss. 1. pp. 52-66. See p. 62.
FORMULA
1 - 6/Pi^2 Sum_{j=0..5} delta_j, where delta_0 = 1 and delta_j = (1/j)* Sum_{i=1..j} (-1)^(i-1) eta_i delta_{j-i}.
EXAMPLE
0.0000000155377352117679639022335262675814992572444423241569849361213...
Sum_{j=0..5} delta_j = 1.64493404128967646496804948687389729523...
MATHEMATICA
digits = 105;
delta[1] = eta[1] = N[Sum[PrimeZetaP[2n], {n, 1, 4 digits}], digits];
eta[2] = N[Sum[n PrimeZetaP[2n+2], {n, 1, 4 digits}] , digits];
eta[3] = N[Sum[n(n+1)/2 PrimeZetaP[2n+4], {n, 1, 4 digits}], digits];
eta[4] = N[Sum[n(n+1)(n+2)/6 PrimeZetaP[2n+6], {n, 1, 4 digits}], digits];
eta[5] = N[Sum[n(n-1)(n-2)(n-3)/24 PrimeZetaP[2n+2], {n, 1, 4 digits}], digits];
delta[0]=1; delta[j_] := 1/j Sum[(-1)^(i-1) eta[i] delta[j-i], {i, 1, j}];
d = 1 - 6/Pi^2 Sum[delta[j], {j, 0, 5}];
RealDigits[d][[1]]
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jean-François Alcover, Mar 18 2019
STATUS
approved