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A215344 Value of x in the n-th number of the form x+y*(1+sqrt(5))/2. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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]

LINKS

Peter G. Anderson, Table of n, a(n) for n = 1..1571

EXAMPLE

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.

PROG

(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 */

CROSSREFS

A215345 is the value of y.

Sequence in context: A334312 A087469 A022328 * A025641 A025649 A025642

Adjacent sequences:  A215341 A215342 A215343 * A215345 A215346 A215347

KEYWORD

nonn

AUTHOR

Peter G. Anderson, Aug 08 2012

STATUS

approved

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)