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

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