cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A068521 Decimal expansion of agm(1, 2).

Original entry on oeis.org

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

Views

Author

Benoit Cloitre, Mar 21 2002

Keywords

Comments

This is the arithmetic-geometric mean of 1 and 2, given by u(1) = 1, v(1) = 2, u(n+1) = (u(n)+v(n))/2, v(n+1) = sqrt(u(n)*v(n)); agm(1,2) = lim u(n) = lim v(n).
Schneider proved that this constant is transcendental. - Charles R Greathouse IV, Feb 03 2025

Examples

			1.45679103104690686918643238326508197497386394322130559079417238326792645458025...

Links

Crossrefs

Cf. A084895 (agm(1,3)), A084896 (agm(1,4)), A084897 (agm(1,5)), A000796, A249283.

Programs

  • Maple
    evalf(GaussAGM(1, 2), 144);  # Alois P. Heinz, Jul 05 2023
evalf(Pi/EllipticK(sqrt(3)/2), 107); # or
evalf(3*Pi/(4*EllipticK(1/3)), 107); # Vaclav Kotesovec, Mar 28 2024
  • Mathematica
    RealDigits[ ArithmeticGeometricMean[1, 2], 10, 107] // First (* Jean-François Alcover, Feb 06 2013 *)
RealDigits[N[3Pi/(4EllipticK[1/9]), 107]][[1]] (* Jean-François Alcover, Jun 02 2019 *)
RealDigits[N[Pi/EllipticK[3/4], 107]][[1]] (* or *)
RealDigits[N[Pi/(2*EllipticK[-3]), 107]][[1]] (* Vaclav Kotesovec, Mar 28 2024 *)
  • PARI
    agm(1,2) \\ Charles R Greathouse IV, Mar 03 2016

Formula

Equals Pi/EllipticK(3/4) = A000796 / A249283. - Amiram Eldar, Apr 28 2025

A084895 Decimal expansion of agm(1, 3), the arithmetic-geometric mean of 1 and 3.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Jun 10 2003

Keywords

Examples

			1.8636167832448965423556890310242705951575328568268537222204412269783257945...

Links

Crossrefs

Cf. A068521 (agm(1,2)), A084896 (agm(1,4)), A084897 (agm(1,5)), A000796, A249282.

Programs

Formula

Equals Pi/EllipticK(1/4) = A000796 / A249282. - Amiram Eldar, Apr 28 2025

A084897 Decimal expansion of agm(1,5), the arithmetic-geometric mean of 1 and 5.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Jun 10 2003

Keywords

Examples

			2.6040081905309402886964274487250343309270652556376494877484132544556792805685...

Links

Crossrefs

Cf. A068521 (agm(1,2)), A084895 (agm(1,3)), A084896 (agm(1,4)).

Programs

Showing 1-3 of 3 results.

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