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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A215344 Value of x in the n-th number of the form x+y*(1+sqrt(5))/2.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 8, 0, 5, 2, 7, 4, 9, 1, 6, 3, 8, 0, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 0, 13, 5, 10, 2, 7, 12, 4, 9, 1, 14, 6, 11, 3, 8, 0, 13, 5, 10, 2, 15, 7, 12, 4, 9, 1, 14, 6, 11, 3, 16, 8, 0, 13, 5, 10, 2, 15, 7, 12, 4, 17, 9, 1, 14, 6, 11, 3, 16, 8, 0, 13, 5
Offset: 1

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Author

Peter G. Anderson, Aug 08 2012

Keywords

Comments

Let x>=0, y>=0 be integers, sort according to x+y*(1+sqrt(5))/2, this sequence gives the x-values. [Joerg Arndt, Aug 16 2012]
The positive elements of this sequence are A084531. [Peter G. Anderson, Aug 28 2012]

Examples

			Let g = (1+sqrt(5))/2, sequences A215344 (x) and A215345 (y) start as:
[x+y*g, x, y]
[0.0000000, 0, 0]
[1.0000000, 1, 0]
[1.6180340, 0, 1]
[2.0000000, 2, 0]
[2.6180340, 1, 1]
[3.0000000, 3, 0]
[3.2360680, 0, 2]
[3.6180340, 2, 1]
[4.0000000, 4, 0]
[4.2360680, 1, 2]
[4.6180340, 3, 1]
[4.8541020, 0, 3]
[5.0000000, 5, 0]
[5.2360680, 2, 2]
[5.6180340, 4, 1]
- _Joerg Arndt_, Aug 17 2012.
		

Crossrefs

A215345 is the value of y.

Programs

  • PARI
    default(realprecision,99); /* using floats */
    g=(1+sqrt(5))/2; /* golden ratio */
    M = 100.0;  /* search limit:  x + y * g <= M */
    v=vector(ceil(M)^2);
    ct=0;
    { for (x=0, M,
        for (y=0, (M-x)/g,
            ct += 1;
            v[ct] = [x+y*g, x, y];
        );
    ); }
    v=vector(ct, n, v[n]);
    v=vecsort(v,1); /* sort according to x + y * g */
    v215344=vector(#v,n,v[n][2])
    v215345=vector(#v,n,v[n][3])
    /* Joerg Arndt, Aug 17 2012 */
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