A003881 -id:A003881 - cp's OEIS frontend

A052146 a(n) = floor((sqrt(1+8*n)-3)/2).

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11

Offset: 1

N. J. A. Sloane, Jan 23 2000

Richard P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge, 1999; see p. 450, Problem 7.2(d).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A003056, A003881.

Floor[(Sqrt[1 + 8 Range[100]] - 3)/2] (* Wesley Ivan Hurt, Oct 02 2021 *)

a(n) = (sqrtint(1 + 8*n)-3)\2; \\ Amiram Eldar, Jun 27 2025

From Amiram Eldar, Jun 27 2025: (Start)
a(n) = A003056(n) - 1.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/4 (A003881). (End)

A096954 Numerators of rational approximation to Pi/4 from Machins's formula.

Original entry on oeis.org

951, 1339849258, 9569810428334921, 19132121777295048135244, 81963468350564671450762204559, 1287504688596138051498743351405666674, 23901655485793371607250742363386659018053931

Offset: 0

Wolfdieter Lang, Jul 23 2004

Machin's formula: Pi/4 = 4*arctan(1/5) - arctan(1/239).

Denominators are given in A096955.

			a(2)/A096955(2) = 9569810428334921/12184551018734375 = .78540...

W. Walter, Analysis I (in German), Springer, 3. Auflage, 1992; p. 216.

Wolfdieter Lang, More comments.
Eric Weisstein's World of Mathematics, Machin's Formula.

Cf. A003881, A096955.

a(n)=numerator(M(n)), with M(n)=4*arctan(1/5, n) - arctan(1/239, n) with arctan(x, n):=sum((((-1)^k)*x^(2k+1))/(2*k+1), k=0..n).

A105531 Decimal expansion of arctan(1/3).

Original entry on oeis.org

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

Offset: 0

Bryan Jacobs (bryanjj(AT)gmail.com), Apr 12 2005

arctan(1/3) + A073000 = 2*arctan(1/3) + A105533 = Pi/4.

			0.3217505543966421934014046143...

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 242.

Peter Bala, New series for old functions
Kunle Adegoke, Infinite arctangent sums involving Fibonacci and Lucas numbers, arXiv:1603.08097 [math.NT], 2016.
Eric Weisstein's World of Mathematics, Machin-Like Formulas
Index entries for transcendental numbers

Cf. A003881 (Pi/4), A073000 (arctan(1/2)), A105533 (arctan(1/7)).

RealDigits[ArcTan[1/3],10,120][[1]] (* Harvey P. Dale, Oct 28 2011 *)

PARI
```
atan(1/3) \\ Michel Marcus, Mar 29 2016
```

From Peter Bala, Feb 04 2015: (Start)
Equals (1/3)*Sum_{k >= 0} (-1)^k/((2*k + 1)*9^k).
Define a pair of integer sequences A(n) = 9^n*(2*n + 1)!/n! and B(n) = A(n)*Sum_{k = 0..n} (-1)^k/((2*k + 1)*9^k). Both sequences satisfy the same recurrence equation u(n) = (32*n + 20)*u(n-1) + 36*(2*n - 1)^2*u(n-2). From this observation we find the continued fraction expansion arctan(1/3) = (1/3)*(1 - 2/(54 + 36*3^2/(84 + 36*5^2/(116 + ... + 36*(2*n - 1)^2/((32*n + 20) + ...))))).
Equals (3/10) * Sum_{k >= 0} (2/5)^k/( (2*k + 1)*binomial(2*k,k) ).
Define a pair of integer sequences C(n) = 10^n*(2*n + 1)!/n! and D(n) = C(n)*Sum_{k = 0..n} (2/5)^k/( (2*k + 1)*binomial(2*k,k) ). Both sequences satisfy the same recurrence equation u(n) = (44*n + 20)*u(n-1) - 80*n*(2*n - 1)*u(n-2). From this observation we obtain the continued fraction expansion arctan(1/3) = (3/10)*( 1 + 4/(60 - 480/(108 - 1200/(152 - ... - 80*n*(2*n - 1)/((44*n + 20) - ...))))). (End)
Equals Sum_{k>=1} arctan(L(4*k+2)/F(4*k+2)^2) where L=A000032 and F=A000045. See also A033890 and A246453. - Michel Marcus, Mar 29 2016 [corrected by Jason Yuen, Jan 18 2025]
From Amiram Eldar, Aug 09 2020: (Start)
Equals Sum_{k>=2} arctan(1/(2*k^2)) = Sum_{k>=2} (-1)^k arctan(2/k^2).
Equals Integral_{x=1..2} 1/(x^2 + 1) dx. (End)
Equals Sum_{n>=0} arctan(1/F(2*n+5)) = Sum_{n>=0} (-1)^n arctan(F(2*n+1)) where F=A000045. - Gleb Koloskov, Oct 01 2021

A113406 Half the number of integer solutions to x^2 + 4 * y^2 = n.

Original entry on oeis.org

1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 0, 0, 4, 0

Offset: 1

Michael Somos, Oct 28 2005

			x + 2*x^4 + 2*x^5 + 2*x^8 + x^9 + 2*x^13 + 2*x^16 + 2*x^17 + 4*x^20 + ...

B. C. Berndt, Ramanujan's Notebooks Part V, Springer-Verlag, see p. 373 Entry 32.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A003881, A004018, A004531, A008441.

s = (EllipticTheta[3, 0, q]*EllipticTheta[3, 0, q^4] - 1)/(2 q) + O[q]^105; CoefficientList[s, q] (* Jean-François Alcover, Dec 02 2015 *)

{a(n) = if( n<1, 0, qfrep( [1, 0; 0, 4], n)[n])}

{a(n) = if( n<1, 0, if( n%4==1, sumdiv( n, d, (-1)^(d\2)), if( n%4==0, 2 * sumdiv( n, d, kronecker( -4, d)))))}

{a(n) = local(A, p, e); if( n<1, 0, A = factor(n); prod( k=1, matsize(A)[1], if( p = A[k,1], e = A[k,2]; if( p==2, 2 * (e>1), if( p%4==3, (1 + (-1)^e) / 2, e+1)))))}

a(n) is multiplicative with a(2) = 0, a(2^e) = 2 if e>1, a(p^e) = e+1 if p == 1 (mod 4), a(p^e) = (1 + (-1)^e)/2 if p == 3 (mod 4)
G.f.: (theta_3(q) * theta_3(q^4) - 1) / 2.
a(4*n + 2) = a(4*n + 3) = 0. A004531(n) = 2 * a(n) if n>0. a(4*n + 1) =  A008441(n). A004018(n) = 2 * a(4*n) if n>0.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/4 = 0.785398... (A003881). - Amiram Eldar, Oct 15 2022

A196521 Decimal expansion of Pi/4-log(2)/2.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Oct 03 2011

			0.438824573117475654907044785090787437011542282663648828183396143330257...

L. B. W. Jolley, Summation of series, Dover Publications Inc., New York, 1961, p. 14 (eq. 72).

Jean-Paul Allouche and Jeffrey Shallit, Sums of digits and the Hurwitz zeta function, in: K. Nagasaka and E. Fouvry (eds.), Analytic Number Theory, Lecture Notes in Mathematics, Vol. 1434, Springer, Berlin, Heidelberg, 1990, pp. 19-30.

Cf. A003881, A016655 (10*log(2)/2), A033264.

Cf. A231902 (Pi/4+log(2)/2), A342316.

Digits:=100; evalf(Pi/4-log(2)/2); # Wesley Ivan Hurt, Dec 06 2013

RealDigits[Pi/4 - Log[2]/2, 10, 100] (* Wesley Ivan Hurt, Dec 06 2013 *)

Pi/4-log(2)/2 \\ Altug Alkan, Dec 14 2015

Equals 1 - 1/2 - 1/3 + 1/4 + 1/5 - ....
Equals Sum_{n>=0} 2/((4*n+2)*(4*n+3)). - Peter Luschny, Dec 06 2013
Equals Sum_{n>=1} (-1)^(n+1)/((2*n-1)*(2*n)). - Robert FERREOL, Dec 14 2015
Equals Integral_{x=0..1} (arctan(x)) dx = Integral_{x=0..Pi/4} (x / cos(x)^2) dx = Integral_{x=0..1/sqrt(2)} (arcsin(x)/(1-x^2)^(3/2)) dx. - Robert FERREOL, Dec 14 2015
Equals Integral_{x>=0} (exp(x) - 1)/(exp(2*x) + 1) dx. - Peter Bala, Nov 01 2019
From Bernard Schott, Sep 07 2020: (Start)
Equals Sum_{n>=1} (-1)^(n*(n-1)/2) / n [compare with A231902 formula].
Equals Sum_{n>=0} (8*n+5) / (4*(n+1)*(2*n+1)*(4*n+1)*(4*n+3)). (End)
Equals Sum_{k>=1} A033264(k)/(k*(k+1)) (Allouche and Shallit, 1990). - Amiram Eldar, Jun 01 2021
From Peter Bala, Mar 04 2025: (Start)
Equals (1/2) * A342316.
Equals Integral_{x = 0..1} x/(x^2 - 2*x + 2) = Integral_{x = 0..1} x*(1 + x)/(2 - x^2*(1 - x)) dx.
Equals (5/2)*Sum_{n >= 1} 1/(n*binomial(3*n, n)*2^n). The first 10 terms of the series gives the approximate value 0.43882457311(68...), correct to 11 decimal places. (End)

A196522 Decimal expansion of Pi*(1+sqrt(2))/8.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Oct 03 2011

This is the mean of two Dirichlet L=functions modulo m=8 at s=1, one with character (1,0,-1,0,1,0,-1,0) as in A101455, the other with character (1,0,1,0,-1,0,-1,0).

The area of a circle circumscribed in a unit-area regular octagon. - Amiram Eldar, Nov 05 2020

			0.948059448968519935684815...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.1, p. 20.
L. B. W. Jolley, Summation of series, Dover (1961), eq. 78 page 16 and eq. 264 page 48.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(1+Sqrt(2))/8; // G. C. Greubel, Oct 05 2018

RealDigits[Pi*(1+Sqrt[2])/8,10,120][[1]] (* Harvey P. Dale, May 31 2013 *)

default(realprecision, 100); Pi*(1+sqrt(2))/8 \\ G. C. Greubel, Oct 05 2018

Equals (1 - 1/7) + (1/9 - 1/15) + ... + (1/(1+8*k) - 1/(7+8*k)) + ... = (A093954 + A003881)/2.

Equals Sum_{n >= 0} (8*k + 6)/((8*n + 1)*(8*n + 8*k + 7)) - Sum_{n = 0..k-1} 1/(8*n + 7), for positive integer k. - Peter Bala, Jul 10 2024

A244978 Decimal expansion of Pi/32.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Jul 09 2014

			0.0981747704246810387019576057274844651311615437304720569054670185096...

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), Chapter 13 A Master Formula, p. 250.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Beta Function
Eric W. Weisstein, Euler's Series Transformation.
Index entries for transcendental numbers

Cf. A019683, A244976, A244977, A019675, A000796, A003881, A019669, A019670, A019683.

Join[{0}, RealDigits[Pi/32, 10, 105] // First]

Pi/32 \\ Charles R Greathouse IV, Sep 28 2022

Equals Integral_{x = 0..1} x^2/(1 + x^2)^3 dx.
Also equals beta(3/2, 1/2)/16, where 'beta' is Euler's beta function.
From Peter Bala, Oct 27 2019: (Start)
Equals Integral_{x = 0..1} x^4*sqrt(1 - x^2) dx = Integral_{x = 0..1} x^5*sqrt(1 - x^4) dx = Integral_{x = 0..1} x^7*sqrt(1 - x^16) dx.
Equals Integral_{x >= 0} x^4/(1 + x^2)^4 dx. (End)
From Amiram Eldar, Jul 13 2020: (Start)
Equals Integral_{x=0..oo} dx/(x^2 + 4)^2.
Equals Sum_{k>=1} sin(k)^3*cos(k)^3/k. (End)
From  Peter Bala, Dec 08 2021: (Start)
Pi/32 = Sum_{n >= 1} (-1)^n*n^2/((4*n^2 - 1)*(4*n^2 - 9)).
Applying Euler's series transformation to this alternating sum gives
Pi/32 = Sum_{n >= 1} 2^(n-3)*n*(n+1)/((2*n+3)*binomial(2*n+2, n+1)). (End)

A199401 Decimal expansion of constant Product_{p>=3} (1 - (-1)^((p-1)/2)/(p-1)). Hardy-Littlewood constant of x^2 + 1.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Nov 05 2011

Arises in studying A002496.

The constant is Product_{primes p} (1-chi(p)/(p-1)) where chi is the Dirichlet character A101455. Its Euler expansion is (1/(L(m=4,r=2,s=1)* zeta(m=4,n=3,s=2)) *Product_{s>=2} zeta(m=4,n=1,s)^gamma(s), where L and zeta are the functions tabulated in arXiv:1008.2547 and gamma is the sequence A001037. In particular L(m=4,r=2,s=1) = A003881 and zeta(m=4,n=1,s=2)=A175647. - R. J. Mathar, Nov 29 2011

			1.372813462818246009112192696727...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.1, p. 85.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 264.

T. Amdeberhan, L. A. Median, and V. H. Moll, Arithmetical properties of a sequence arising from an arctangent sum, J. Numb. Theory 128 (2008) 1807-1846, eq. (1.10).
Karim Belabas and Henri Cohen, Computation of the Hardy-Littlewood constant for quadratic polynomials, PARI/GP script, 2020.
Henri Cohen, High-precision computation of Hardy-Littlewood constants, (1998). [pdf copy, with permission]
G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70. See Section 5.41.
Richard J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.
Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 2008-2010.

Cf. A002496.
Cf. A001037, A003881, A083844, A175647, A221712, A331942.
Equals 2*constant given by A331941.

\\ See Belabas, Cohen link. Run as HardyLittlewood2(x^2+1) after setting the required precision.

Extended title, a(30) and beyond from Hugo Pfoertner, Feb 16 2020

A240935 Decimal expansion of 3sqrt(3)/(4Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Aug 03 2014

A triangle of maximal area inside a circle is necessarily an inscribed equilateral triangle. This constant is the ratio of the triangle's area to the circle's area. In general, the ratio of an arbitrary triangle's area to the area of its unique Steiner ellipse, which has the least area of any circumscribed ellipse (an equilateral triangle's Steiner ellipse is a circle).

Also the probability that the distance between 2 randomly selected points within a circle will be larger than the radius. - Amiram Eldar, Mar 03 2019

			0.4134966715663440371334948737347270810480...

B. F. Finkel, Problem 38, solved by O. W. Anthony, Henry Heaton, and G. B. M. Zerr, The American Mathematical Monthly, Vol. 3, No. 12 (1896), pp. 324-326.
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), p.52
I. Todhunter, A treatise on the Integral Calculus, London and Cambridge: MacMillan and Co., 1868, page 320, Example 7.
Wikipedia, Steiner ellipse
Index entries for transcendental numbers

Cf. A073010, A060294, A003881, A002194, A000796, A102519, A086089.

Digits:=100: evalf(3*sqrt(3)/(4*Pi)); # Wesley Ivan Hurt, Aug 03 2014

Flatten[RealDigits[3 Sqrt[3]/(4 Pi), 10, 100, -1]] (* Wesley Ivan Hurt, Aug 03 2014 *)

default(realprecision, 120);
3*sqrt(3)/(4*Pi)

3*sqrt(3)/(4*Pi) = 3*A002194/(4*A000796).

Equals A093604^2. - Hugo Pfoertner, May 18 2024

A381152 Decimal expansion of the isoperimetric quotient of a regular pentagon.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Feb 15 2025

The isoperimetric quotient of a closed curve is equal to 4*Pi*A/p^2, where A is the area enclosed by the curve and p is its perimeter. For a regular n-gon, this is equivalent to Pi/(n*tan(Pi/n)).

The isoperimetric quotient of a circle is 1.

			0.86480626597720996723118206585862333703828555690228...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Isoperimetric Quotient.
Wikipedia, Isoperimetric inequality.

Cf. A019952, A102771.

Cf. isoperimetric quotient of other regular polygons: A073010 (triangle), A003881 (square), A093766 (hexagon), A381153 (heptagon), A196522 (octagon), A381154 (9-gon), A381155 (10-gon), A381156 (11-gon), A381157 (12-gon).

First[RealDigits[Pi/(5*Tan[Pi/5]), 10, 100]]

Equals Pi/(5*tan(Pi/5)) = (Pi/5)*A019952.

Equals (4/25)*Pi*A102771.

cp's OEIS Frontend

A052146 a(n) = floor((sqrt(1+8*n)-3)/2).

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A096954 Numerators of rational approximation to Pi/4 from Machins's formula.

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A105531 Decimal expansion of arctan(1/3).

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A113406 Half the number of integer solutions to x^2 + 4 * y^2 = n.

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A196521 Decimal expansion of Pi/4-log(2)/2.

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A196522 Decimal expansion of Pi*(1+sqrt(2))/8.

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A244978 Decimal expansion of Pi/32.

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A240935 Decimal expansion of 3sqrt(3)/(4Pi).