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.

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A191334 Decimal expansion of sum{(1/3)^A005653(k): k>=1}.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 31 2011

Keywords

Comments

sum{(1/3)^A005653(k)}+sum{(1/3)^A005652(k)}=1/2.

Examples

			0.128048780393371654692958265098687655...

Crossrefs

Cf. A191329, A191335.

Programs

A078796 a(n) = 2*ceiling(n*tau) - ceiling(n*sqrt(5)) where tau=(1+sqrt(5))/2 is the Golden ratio.

Original entry on oeis.org

1, 3, 3, 5, 6, 6, 8, 8, 9, 11, 11, 13, 14, 14, 16, 16, 17, 19, 19, 21, 21, 22, 24, 24, 26, 27, 27, 29, 29, 30, 32, 32, 34, 35, 35, 37, 37, 39, 40, 40, 42, 42, 43, 45, 45, 47, 48, 48, 50, 50, 51, 53, 53, 55, 55, 56, 58, 58, 60, 61, 61, 63, 63, 64, 66, 66, 68, 69, 69, 71, 71, 73
Offset: 1

Views

Author

Benoit Cloitre, Dec 05 2002

Keywords

Crossrefs

Cf. A001950, A005652, A078588.

Programs

  • Mathematica
    Table[2*Ceiling[n*GoldenRatio]-Ceiling[n*Sqrt[5]],{n,80}] (* Harvey P. Dale, Dec 20 2015 *)
  • PARI
    a(n)=2*ceil(n*(1+sqrt(5))/2)-ceil(n*sqrt(5))
  • Python
    from math import isqrt
def A078796(n): return (n+(m:=isqrt(5*n**2))&-2)-m+1 # Chai Wah Wu, Aug 17 2022

Formula

a(A005652(n)) = A005652(n); a(A001950(n)) = A001950(n) + 1.

A138683 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n) and a(k) do not sum to a term of A001333 (Numerators of continued fraction convergents to sqrt(2)).

Original entry on oeis.org

2, 3, 6, 7, 8, 12, 13, 16, 17, 18, 19, 20, 26, 27, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 64, 65, 66, 70, 71, 74, 75, 76, 77, 78, 84, 85, 88, 89, 90, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115
Offset: 1

Views

Author

John W. Layman, Mar 26 2008

Keywords

Comments

The graph of the first differences (A138684) of this sequence is fractal-like.

Crossrefs

Cf. A001333, A005652, A114889, A138684.

A367491 Lexicographically least increasing sequence, starting with 2, such that no two terms (possibly identical) sum to a Fibonacci number.

Original entry on oeis.org

2, 5, 7, 9, 10, 13, 15, 18, 20, 22, 23, 26, 28, 30, 31, 34, 36, 38, 39, 41, 43, 44, 47, 49, 52, 54, 56, 57, 60, 62, 64, 65, 68, 70, 73, 75, 77, 78, 81, 83, 85, 86, 89, 91, 93, 94, 96, 98, 99, 102, 104, 107, 109, 111, 112, 115, 117, 119, 120, 123, 125, 127, 128
Offset: 1

Views

Author

Jeffrey Shallit, Nov 20 2023

Keywords

Comments

There is an 8-state Fibonacci automaton that accepts the Zeckendorf representation of n if and only if n belongs to the sequence.

Examples

			6 is not in the sequence, since if it were, 6+2 = 8, a Fibonacci number.

Crossrefs

Cf. A005652, A005653. This sequence allows the same term to be used twice in the sum, whereas in the other two sequences, the terms must be distinct.
Previous Showing 21-24 of 24 results.

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

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