A256425 -id:A256425 - cp's OEIS frontend

A001817 G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).

1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 2, 1, 3, 3, 3, 1, 4, 1, 1, 2, 4, 2, 2, 1, 3, 2, 2, 2, 4, 2, 2, 2, 3, 1, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 5, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 4, 3, 2, 2, 2, 3, 2, 3, 1, 5, 1, 2, 2, 4, 2

Offset: 1

N. J. A. Sloane

a(n) is the number of positive divisors of n of the form 3k+1. If r(n) denotes the number of representations of n by the quadratic form j^2+ij+i^2, then r(n)= 6 *(a(n)-A001822(n)). - Benoit Cloitre, Jun 24 2002

			x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + x^9 + ...

Bruce C. Berndt, On a certain theta-function in a letter of Ramanujan from Fitzroy House, Ganita 43 (1992), 33-43.

Nick Hobson, Table of n, a(n) for n = 1..10000
P. G. Dirichlet, Recherches sur diverses applications de l'analyse infinitésimale à la théorie des nombres, J. Reine Angew. Math. 21 (1840), 1-12.
Michael Gilleland, Some Self-Similar Integer Sequences.
R. A. Smith and M. V. Subbarao, The average number of divisors in an arithmetic progression, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.

Cf. A001822, A035191, A002324.
Cf. A051731.
Cf. A001620, A256425.

a001817 n = length [d | d <- [1,4..n], mod n d == 0]
-- Reinhard Zumkeller, Nov 26 2011

A001817 := proc(n)
    local a,d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if modp(d,3) = 1 then
            a := a+1 ;
        end if ;
    end do:
    a ;
end proc:
seq(A001817(n),n=1..100) ; # R. J. Mathar, Sep 25 2017

a[n_] := DivisorSum[n, Boole[Mod[#, 3] == 1]&]; Array[a, 100] (* Jean-François Alcover, Dec 01 2015 *)

PARI
```
a(n)=if(n<1,0,sumdiv(n,d,d%3==1))
```

Moebius transform is period 3 sequence [1, 0, 0, ...]. - Michael Somos, Sep 20 2005
G.f.: Sum_{k>0} x^(3k-2)/(1-x^(3k-2)) = Sum_{k>0} x^k/(1-x^(3k)). - Michael Somos, Sep 20 2005
Equals A051731 * [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...]. - Gary W. Adamson, Nov 06 2007
a(n) = (A035191(n) + A002324(n)) / 2. - Reinhard Zumkeller, Nov 26 2011
Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

A256778 Decimal expansion of the generalized Euler constant gamma(1,4).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			0.71028979306409369731376647579508261030406104249693294...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.3, p. 32.

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016627, A020777, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256779-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

R:=RealField(100); (2*EulerGamma(R) + Pi(R) + 2*Log(2))/8; // G. C. Greubel, Aug 27 2018

RealDigits[EulerGamma/4 + Pi/8 + Log[2]/4, 10, 103] // First

default(realprecision, 100); (2*Euler + Pi + 2*log(2))/8 \\ G. C. Greubel, Aug 27 2018

Equals (2*EulerGamma + Pi + 2*log(2))/8.
Equals Sum_{n>=0} (1/(4n+1) - 1/2*arctanh(2/(4n+3))).
Equals -(psi(1/4) + log(4))/4 = (A020777 - A016627)/4. - Amiram Eldar, Jan 07 2024

A256784 Decimal expansion of the generalized Euler constant gamma(5,12) (negated).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			-0.0033729493224032970250324948185921946160340346994983953873167...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016635, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/12 + 1/24*(Pi(R)*(2-Sqrt(3)) + 2*(Sqrt(3)+1)*Log(2) + Log(3) - 4*Sqrt(3)*Log(Sqrt(3)+1)); // G. C. Greubel, Aug 27 2018

Join[{0, 0}, RealDigits[-Log[12]/12 - PolyGamma[5/12]/12, 10, 105] // First]

default(realprecision, 100); Euler/12 + 1/24*(Pi*(2-sqrt(3)) + 2*(sqrt(3)+1)*log(2) + log(3) - 4*sqrt(3)*log(sqrt(3)+1)) \\ G. C. Greubel, Aug 27 2018

Equals EulerGamma/12 + 1/24*(Pi*(2-sqrt(3)) + 2*(sqrt(3)+1)*log(2) + log(3) - 4*sqrt(3) * log(sqrt(3)+1)).

Equals -(psi(5/12) + log(12))/12. - Amiram Eldar, Jan 07 2024

A256779 Decimal expansion of the generalized Euler constant gamma(1,5).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			0.735920396831617584189289725844752893059997383987625...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016628, A200135, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/10*Sqrt(1 + 2/Sqrt(5)) + Log(5)/20 + Sqrt(5)/10*Log((1 + Sqrt(5))/2); // G. C. Greubel, Aug 28 2018

RealDigits[-Log[5]/5 - PolyGamma[1/5]/5, 10, 105] // First

Euler/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2) \\ Michel Marcus, Apr 10 2015

Equals EulerGamma/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2).
Equals Sum_{n>=0} (1/(5n+1) - 2/5*arctanh(5/(10n+7))).
Equals -(psi(1/5) + log(5))/5 = (A200135 - A016628)/5. - Amiram Eldar, Jan 07 2024

A256843 Decimal expansion of the generalized Euler constant gamma(2,3).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 11 2015

			0.07320737570615959366903185990752913907462383026830934562939...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (gamma(1,1) = EulerGamma), A002391, A200064.
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).
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).

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/3 - Pi(R)/(6*Sqrt(3)) + Log(3)/6; // G. C. Greubel, Aug 28 2018

Join[{0}, RealDigits[-Log[3]/3 - PolyGamma[2/3]/3, 10, 105] // First]

default(realprecision, 100); Euler/3 - Pi/(6*sqrt(3)) + log(3)/6 \\ G. C. Greubel, Aug 28 2018

Equals EulerGamma/3 - Pi/(6*sqrt(3)) + log(3)/6.

Equals -(psi(2/3) + log(3))/3 = (A200064 - A002391)/3. - Amiram Eldar, Jan 07 2024

A256780 Decimal expansion of the generalized Euler constant gamma(2,5).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			0.190389326430203154225983229764268163260151948448458487...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016628, A200136, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/10*Sqrt(1 - 2/Sqrt(5)) + Log(5)/20 - Sqrt(5)/10*Log((1 + Sqrt(5))/2); // G. C. Greubel, Aug 28 2018

RealDigits[-Log[5]/5 - PolyGamma[2/5]/5, 10, 105] // First

Euler/5 + Pi/10*sqrt(1 - 2/sqrt(5)) + log(5)/20 - sqrt(5)/10*log((1 + sqrt(5))/2) \\ Michel Marcus, Apr 10 2015

Equals EulerGamma/5 + Pi/10*sqrt(1 - 2/sqrt(5)) + log(5)/20 - sqrt(5)/10*log((1 + sqrt(5))/2).
Equals Sum_{n>=0} (1/(5n+2) - 2/5*arctanh(5/(10n+9))).
Equals -(psi(2/5) + log(5))/5 = (A200136 - A016628)/5. - Amiram Eldar, Jan 07 2024

A256781 Decimal expansion of the generalized Euler constant gamma(1,8).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			0.788631390202002367443880819838976661978118204921...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016631, A228725 (gamma(1,2)), A250129, A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/8 + (1/8)*(Pi(R)/2*(Sqrt(2)+1) + Log(2) + Sqrt(2)*Log(Sqrt(2) + 1)); // G. C. Greubel, Aug 28 2018

RealDigits[-3/8*Log[2] - PolyGamma[1/8]/8, 10, 105] // First

Euler/8 + 1/8*(Pi/2*(sqrt(2)+1) + log(2) + sqrt(2)*log(sqrt(2) + 1)) \\ Michel Marcus, Apr 10 2015

Equals EulerGamma/8 + 1/8*(Pi/2*(sqrt(2)+1) + log(2) + sqrt(2)*log(sqrt(2) + 1)).
Equals Sum_{n>=0} (1/(8n+1) - 1/4*arctanh(4/(8n+5))).
Equals -(psi(1/8) + log(8))/8 = -(A250129 + A016631)/8. - Amiram Eldar, Jan 07 2024

A256782 Decimal expansion of the generalized Euler constant gamma(3,8).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 10 2015

			0.08431968843316295593904035680375480012812437382591706852303...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), p. 134.

Cf. A001620 (EulerGamma), A016631, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)), A354633.

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/8 + (1/8)*(Pi(R)/2*(Sqrt(2)-1) + Log(2) - Sqrt(2)*Log(Sqrt(2)+1)); // G. C. Greubel, Aug 28 2018

Join[{0}, RealDigits[-3/8*Log[2] - PolyGamma[3/8]/8, 10, 104] // First]

default(realprecision, 100); Euler/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)) \\ G. C. Greubel, Aug 28 2018

Equals EulerGamma/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)).

Equals -(psi(3/8) + log(8))/8 = -(A354633 + A016631)/8. - Amiram Eldar, Jan 07 2024

A256845 Decimal expansion of the generalized Euler constant gamma(2,4).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 11 2015

			0.1443039162253832151516280225206006077605398339849808997...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134.

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

R:= RealField(100); EulerGamma(R)/4; // G. C. Greubel, Aug 28 2018

RealDigits[EulerGamma/4, 10, 107] // First

default(realprecision, 100); Euler/4 \\ G. C. Greubel, Aug 28 2018

-log(4)/4 - PolyGamma(1/2)/4 = EulerGamma/4
From Amiram Eldar, Jul 21 2020: (Start)
Equals -Integral_{x=0..oo} e^(-x^2)*x*log(x) dx.
Equals Integral_{x=0..oo} (e^(-x^4) - e^(-x^2))/x dx. (End)

A256846 Decimal expansion of the generalized Euler constant gamma(3,4) (negated).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 11 2015

			-0.07510837033335461230189437002479311074523130734684351439...

G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134.

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

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/4 - Pi(R)/8 - Log(4)/4 + Log(8)/4; // G. C. Greubel, Aug 28 2018

Join[{0}, RealDigits[-Log[4]/4 - PolyGamma[3/4]/4, 10, 104] // First ]

default(realprecision, 100); Euler/4 - Pi/8 - log(4)/4 + log(8)/4 \\ G. C. Greubel, Aug 28 2018

-log(4)/4 - PolyGamma(3/4)/4 = EulerGamma/4 - Pi/8 - log(4)/4 + log(8)/4

cp's OEIS Frontend

A001817 G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).

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A256778 Decimal expansion of the generalized Euler constant gamma(1,4).

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A256784 Decimal expansion of the generalized Euler constant gamma(5,12) (negated).

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A256779 Decimal expansion of the generalized Euler constant gamma(1,5).

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A256843 Decimal expansion of the generalized Euler constant gamma(2,3).

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A256780 Decimal expansion of the generalized Euler constant gamma(2,5).

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A256781 Decimal expansion of the generalized Euler constant gamma(1,8).

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