A340884 Decimal expansion of the constant rho(1,5).

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

Offset

0,1

Comments

From definition Steven Finch and Pascal Sebah 2009 p. 1:

rho(n,m) = lim_{s->1} (s-1) Product_{primes p==n (mod m)} (1-1/p^s)^phi(m), where phi(n) = A000010(n) is the Euler totient function.

Links

Table of n, a(n) for n=0..116.

Steven Finch and Pascal Sebah, Residue of a Mod 5 Euler Product, arXiv:0912.3677 [math.NT], 2009 p. 1-2.

Formula

Equals 1/(exp(gamma)*A340839^4).

Formulas by Steven Finch and Pascal Sebah 2009 p. 2.

Equals 5*log(2 + sqrt(5))*A340004^2/(3*Pi^2).

Equals 50*log(2 + sqrt(5))*A340808/(13*Pi^2*sqrt(5)*A340628).

Example

0.249135702764931424659963795...

Crossrefs

Cf. A340628, A340808, A340004.

Sequence in context: A354014 A195729 A303950 * A011181 A134822 A229351

Adjacent sequences: A340881 A340882 A340883 * A340885 A340886 A340887

Keyword

nonn,cons

Author

Artur Jasinski, Jan 25 2021

Status

approved