login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324835 Decimal expansion of eta_4, a constant related to the asymptotic density of certain sets of residues. 4
1, 2, 5, 9, 3, 0, 2, 8, 3, 9, 8, 6, 4, 2, 0, 1, 3, 6, 5, 2, 9, 9, 1, 1, 0, 2, 2, 6, 2, 2, 9, 2, 1, 7, 6, 9, 4, 7, 3, 4, 3, 2, 0, 8, 9, 8, 5, 4, 2, 2, 1, 8, 6, 1, 4, 7, 2, 5, 7, 8, 9, 3, 6, 6, 9, 5, 4, 7, 5, 7, 7, 9, 0, 8, 4, 7, 0, 9, 9, 1, 8, 3, 2, 8, 4, 7, 7, 0, 8, 9, 7, 8, 5, 9, 1, 1, 0, 1, 3, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

Table of n, a(n) for n=-1..99.

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

Sum_{p prime} 1/(p^2-1)^4.

Sum_{n>0} (n(n+1)(n+2)/6) P(2n+6) where P is the prime zeta P function.

EXAMPLE

0.0125930283986420136529911022622921769473432089854221861472578936695...

MATHEMATICA

digits = 101; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta4 = Sum[n(n+1)(n+2)/6 PrimeZetaP[2n+6], {n, 1, m}], 10, digits][[1]]; rd[m0]; rd[m = 2 m0]; While[rd[m] != rd[m-m0], Print[m]; m = m+m0]; Print[N[eta4, digits]]; rd[m]

CROSSREFS

Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324836 (eta_5).

Sequence in context: A019802 A248934 A011432 * A082183 A111474 A111761

Adjacent sequences:  A324832 A324833 A324834 * A324836 A324837 A324838

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Mar 17 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 07:18 EST 2020. Contains 331189 sequences. (Running on oeis4.)