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.

A119505 The Pi-th digit of Pi where the digit value of 0 is interpreted as decimal 10.

Original entry on oeis.org

4, 3, 1, 3, 5, 5, 1, 9, 5, 4, 5, 6, 5, 2, 5, 4, 1, 4, 6, 1, 9, 1, 9, 1, 4, 4, 6, 4, 1, 2, 5, 5, 3, 1, 6, 6, 1, 3, 5, 2, 3, 9, 5, 4, 5, 5, 4, 2, 5, 3, 3, 5, 6, 1, 3, 5, 2, 1, 5, 1, 1, 5, 5, 1, 4, 3, 2, 6, 3, 9, 1, 3, 9, 1, 6, 9, 1, 3, 6, 5, 5, 6, 9, 1, 6, 3, 4, 1, 6, 1, 5, 4, 1, 1, 3, 3, 2, 3, 9, 2, 5, 6, 1, 3, 1
Offset: 1

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Author

Cino Hilliard, May 27 2006

Keywords

Comments

The numbers formed in this sequence are 1,2,3,4,5,6,9. Conjecture: The terms of this sequence are nonrepeating and nonterminating.

Examples

			The digit of Pi in the first position is 3, and the digit of Pi in the third position is 4, the first term in the table.

Links

Programs

  • Mathematica
    id = RealDigits[Pi, 10, 105][[1]]; id[[0]] = 3; Table[id[[id[[n]] ]], {n, 105}] (* Robert G. Wilson v, Mar 17 2009 *)
  • PARI
    g(n)=a=Vec(Str(Pi*10^9990));for(x=1,n,v=eval(a[x]);if(v==0,print1(a[v+10]","),print1(a[v]",")))

Formula

Let the i-th digit of Pi be the digit of Pi in the i-th position. Then the Pi-th digit of Pi is the digit of Pi in the position corresponding to the value of the i-th digit.
a(n) = A000796(A010889(9+A000796(n))). - R. J. Mathar, Feb 23 2009

Extensions

Missing terms a(33), a(55) and a(66) inserted by R. J. Mathar, Feb 23 2009

A177933 Decimal expansion of (232405+sqrt(71216963807))/348378.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 15 2010

Keywords

Comments

Continued fraction expansion of (232405+sqrt(71216963807))/348378 is A010889.
Agrees with A060997 for n < 14, with A177270 for n < 13, with A177034 for n < 11, with A177160 for n < 9.

Examples

			(232405+sqrt(71216963807))/348378 = 1.43312742672229113069...

Links

Crossrefs

Cf. A177934 (decimal expansion of sqrt(71216963807)), A010889 (repeat 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A060997 (decimal representation of continued fraction 1, 2, 3, 4, 5, 6, 7, ...), A177270 (decimal expansion of (684125+sqrt(635918528029))/1033802), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165), A177160 (decimal expansion of (4502+sqrt(29964677))/6961).

Programs

  • Mathematica
    First[RealDigits[(232405+Sqrt[71216963807])/348378,10,120]] (* Paolo Xausa, Jan 09 2024 *)

A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Sep 29 2015

Keywords

Comments

Decimal expansion of 111111112/900000009.
For n which lies in the interval [16*(k-1), 8*(2*k-1)], where k>0 -> pattern {1, 2, 3, 4, 5, 6, 7, 8, 9}; for n which lies in the interval [16*k - 7, 16*k - 1], where k>0 -> pattern {8, 7, 6, 5, 4, 3, 2}.

Links

Crossrefs

Cf. A158289, A177274, A010889, A138531, A181975, A199264, A068073, A028356.

Programs

  • Magma
    &cat[[1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2]: n in [0..10]]; // Vincenzo Librandi, Sep 29 2015
  • Mathematica
    LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9}, 120] (* Vincenzo Librandi, Sep 29 2015 *)
  • PARI
    Vec(-(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)*(x^8+1)) + O(x^100)) \\ Colin Barker, Sep 29 2015
  • PARI
    111111112/900000009. \\ Altug Alkan, Sep 29 2015
  • PARI
    vector(200, n, default(realprecision, n+2); floor(111111112/900000009*10^n)%10) \\ Altug Alkan, Nov 12 2015

Formula

-1 + a(16*(k - 1)) = -2 + a(8*k + 3*(-1)^k - 4) = -3 + a(2*(4*k + (-1)^k - 2)) = -4 + a(8*k + (-1)^k - 4) = -5 + a(4*(2*k - 1)) = -6 + a(8*k - (-1)^k - 4) = -7 + a(-2*(-4*k + (-1)^k + 2)) = -8 + a(8*k - 3*(-1)^k - 4) = -9 + a(8*(2*k - 11)) = 0, for k>0.
a(0) = 1, a(n) = a(n+1) - 1, for 16*(k - 1) <= n < 8*(2*k - 1), and a(n) = a(n + 1) + 1, for 8*(2*k - 1) <= n < 16*k, where k>0.
From Colin Barker, Sep 29 2015: (Start)
a(n) = a(n-1) - a(n-8) + a(n-9) for n>8.
G.f.: -(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(x^8+1)). (End)
Showing 1-3 of 3 results.

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