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
Keywords
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.
Links
- Peter G. Anderson, Table of n, a(n) for n = 1..1571
Crossrefs
A215345 is the value of y.
Programs
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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 */
Comments