cp's OEIS Frontend

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

%I A215344 #21 Aug 28 2012 09:48:58
%S A215344 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,
%T A215344 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,
%U A215344 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
%N A215344 Value of x in the n-th number of the form x+y*(1+sqrt(5))/2.
%C A215344 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]
%C A215344 The positive elements of this sequence are A084531. [_Peter G. Anderson_, Aug 28 2012]
%H A215344 Peter G. Anderson, <a href="/A215344/b215344.txt">Table of n, a(n) for n = 1..1571</a>
%e A215344 Let g = (1+sqrt(5))/2, sequences A215344 (x) and A215345 (y) start as:
%e A215344 [x+y*g, x, y]
%e A215344 [0.0000000, 0, 0]
%e A215344 [1.0000000, 1, 0]
%e A215344 [1.6180340, 0, 1]
%e A215344 [2.0000000, 2, 0]
%e A215344 [2.6180340, 1, 1]
%e A215344 [3.0000000, 3, 0]
%e A215344 [3.2360680, 0, 2]
%e A215344 [3.6180340, 2, 1]
%e A215344 [4.0000000, 4, 0]
%e A215344 [4.2360680, 1, 2]
%e A215344 [4.6180340, 3, 1]
%e A215344 [4.8541020, 0, 3]
%e A215344 [5.0000000, 5, 0]
%e A215344 [5.2360680, 2, 2]
%e A215344 [5.6180340, 4, 1]
%e A215344 - _Joerg Arndt_, Aug 17 2012.
%o A215344 (PARI)
%o A215344 default(realprecision,99); /* using floats */
%o A215344 g=(1+sqrt(5))/2; /* golden ratio */
%o A215344 M = 100.0;  /* search limit:  x + y * g <= M */
%o A215344 v=vector(ceil(M)^2);
%o A215344 ct=0;
%o A215344 { for (x=0, M,
%o A215344     for (y=0, (M-x)/g,
%o A215344         ct += 1;
%o A215344         v[ct] = [x+y*g, x, y];
%o A215344     );
%o A215344 ); }
%o A215344 v=vector(ct, n, v[n]);
%o A215344 v=vecsort(v,1); /* sort according to x + y * g */
%o A215344 v215344=vector(#v,n,v[n][2])
%o A215344 v215345=vector(#v,n,v[n][3])
%o A215344 /* _Joerg Arndt_, Aug 17 2012 */
%Y A215344 A215345 is the value of y.
%K A215344 nonn
%O A215344 1,4
%A A215344 _Peter G. Anderson_, Aug 08 2012