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.

A010477 Decimal expansion of square root of 21.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

Continued fraction expansion is 4 followed by {1, 1, 2, 1, 1, 8} repeated. - Harry J. Smith, Jun 03 2009
The fundamntal algebraic (integer) number in the field Q(sqrt(21)) is (1 + sqrt(21))/2 = A222134. - Wolfdieter Lang, Nov 21 2023

Examples

			4.582575694955840006588047193728008488984456576767971902607242123906868...

Links

Crossrefs

Cf. A010125 (continued fraction), A248249 (Egyptian fraction).
Cf. A020778 (reciprocal), A222134.

Programs

  • Mathematica
    RealDigits[N[Sqrt[21],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)
  • PARI
    default(realprecision, 20080); x=sqrt(21); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010477.txt", n, " ", d));  \\ Harry J. Smith, Jun 03 2009

A106740 Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).

Original entry on oeis.org

2, 1, 3, 1, 1, 5, 2, 1, 1, 8, 1, 1, 1, 1, 13, 1, 3, 1, 1, 1, 21, 2, 1, 1, 2, 1, 1, 34, 1, 1, 5, 1, 1, 1, 1, 55, 1, 1, 1, 1, 1, 1, 1, 1, 89, 2, 3, 1, 8, 1, 3, 2, 1, 1, 144, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 233, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 377, 2, 1, 5, 2, 1, 1, 2, 5, 1, 2, 1, 1, 610
Offset: 3

Views

Author

Reinhard Zumkeller, May 15 2005

Keywords

Examples

			Triangle begins as:
  2;
  1, 3;
  1, 1, 5;
  2, 1, 1, 8;
  1, 1, 1, 1, 13;
  1, 3, 1, 1,  1, 21;
  2, 1, 1, 2,  1,  1, 34;
  1, 1, 5, 1,  1,  1,  1, 55;
  1, 1, 1, 1,  1,  1,  1,  1, 89;
  2, 3, 1, 8,  1,  3,  2,  1,  1, 144;
  1, 1, 1, 1,  1,  1,  1,  1,  1,   1, 233;
  1, 1, 1, 1, 13,  1,  1,  1,  1,   1,   1, 377;
  2, 1, 5, 2,  1,  1,  2,  5,  1,   2,   1,   1, 610;

Links

Crossrefs

Cf. A000012, A000045, A010125, A060904, A061347, A093148, A131534.

Programs

  • Mathematica
    T[n_, k_]:= GCD[Fibonacci[n], Fibonacci[k]];
Table[T[n, k], {n,3,18}, {k,3,n}]//Flatten (* G. C. Greubel, Sep 11 2021 *)
  • Sage
    def T(n,k): return gcd(fibonacci(n), fibonacci(k))
flatten([[T(n,k) for k in (3..n)] for n in (3..18)]) # G. C. Greubel, Sep 11 2021

Formula

T(n, k) = gcd(A000045(n), A000045(k)) for n >= 3 and 3 <= k <= n.
T(n, 3) = abs(A061347(n)).
T(n, 4) = A093148(n-1).
T(n, n) = A000045(n).
From G. C. Greubel, Sep 11 2021: (Start)
T(n, 3) = A131534(n-2).
T(n, 5) = A060904(n).
T(n, 6) = A010125(n).
T(n, n-1) = T(n, n-2) = A000012(n).
T(n, n-3) = A093148(n-5).
T(n, n-4) = A093148(n-5).
T(n, n-5) = A060904(n-5).
T(n, n-6) = A010125(n-6). (End)

A109150 Numbers k such that the continued fraction sequence of sqrt(k) is not multiplicative.

Original entry on oeis.org

2, 5, 6, 10, 11, 12, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 37, 38, 39, 40, 41, 42, 43, 45, 46, 50, 51, 52, 53, 54, 55, 56, 57, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 97, 101, 102, 103, 104, 105, 106, 107
Offset: 1

Views

Author

Mitch Harris, Jun 20 2005

Keywords

Examples

			The continued fraction of sqrt(21) is (4; 1, 1, 2, 1, 1, 8, ...) = A010125, which is not multiplicative since c(2) = 1, c(3) = 2, but c(6) = 8.

Crossrefs

Complement of A109054.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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