A256850 - OEIS

%I #11 Sep 08 2022 08:46:12

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

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

%U 2,2,5,2,1,8,5,9,9,8,6,1,8,7,3,8,6,3,7,3,6,2,9,6,0,2,8,6,5,7,2,2,5,7

%N Decimal expansion of the generalized Euler constant gamma(5,5) (negated).

%H G. C. Greubel, <a href="/A256850/b256850.txt">Table of n, a(n) for n = 0..10000</a>

%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27121.pdf">Euler constants for arithmetic progressions</a>, Acta Arith. 27 (1975) p. 134.

%F Equals (EulerGamma - log(5))/5.

%e -0.20644444950651350279884944862875704169668840366571882462...

%t RealDigits[EulerGamma/5 - Log[5]/5, 10, 102] // First

%o (PARI) default(realprecision, 100); (Euler - log(5))/5 \\ _G. C. Greubel_, Aug 28 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (EulerGamma(R) - Log(5))/5; // _G. C. Greubel_, Aug 28 2018

%Y Cf. A001620 (gamma(1,1) = EulerGamma),

%Y Primitive ruler-and-compass constructible gamma(r,k): A228725 (1,2), A256425 (1,3), A256778 (1,4), A256779 (1,5), A256780 (2,5), A256781 (1,8), A256782 (3,8), A256783 (1,12), A256784 (5,12),

%Y Other gamma(r,k) (1 <= r <= k <= 5): A239097 (2,2),  A256843 (2,3),  A256844 (3,3), A256845 (2,4), A256846 (3,4), A256847 (4,4), A256848 (3,5), A256849 (4,5), A256850 (5,5).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Apr 11 2015