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A183555 Positions of the records of the positive integers in A179319; a(n) is the first position in A179319 equal to +n.

%I A183555 #8 Mar 31 2012 23:00:47
%S A183555 0,15,159,303,2887,5471,51839,98207,930247,1762287,16692639,31622991
%N A183555 Positions of the records of the positive integers in A179319; a(n) is the first position in A179319 equal to +n.
%C A183555  The g.f. of A059973 is (x+x^2-2*x^3)/(1-4*x^2-x^4).
%F A183555 Conjecture: the positions of the records of the positive integers in A179319 are given by:
%F A183555 * a(2n-1) = A059973(4n+1) - 2 for n>1, with a(1) = 0;
%F A183555 * a(2n) = A059973(4n+2) - 2 for n>=1.
%e A183555 Define WL(x) and WU(x) to be respectively the characteristic functions of the lower (A000201) and upper (A001950) Wythoff sequences:
%e A183555 * WL(x) = 1 + x + x^3 + x^4 + x^6 + x^8 + x^9 + x^11 +...+ x^[n*phi] +...
%e A183555 * WU(x) = 1 + x^2 + x^5 + x^7 + x^10 + x^13 + x^15 +...+ x^[n*(phi+1)] +...
%e A183555 Then the g.f. of A179319 is the product:
%e A183555 * WL(-x)*WU(x) = 1 - x + x^2 - 2*x^3 + x^4 + x^6 + x^7 + x^10 - x^11 + x^12 + x^13 + x^14 + 2*x^15 +...+ A179319(n)*x^n +...
%e A183555 in which it is conjectured that the following holds:
%e A183555 * A179319(A059973(4n+1) - 2) = 2n-1 for n>=1;
%e A183555 * A179319(A059973(4n+2) - 2) = 2n for n>=1.
%Y A183555 Cf. A183556, A179319, A059973, A183557, A000201, A001950.
%K A183555 nonn,more
%O A183555 1,2
%A A183555 _Paul D. Hanna_, Jan 12 2011
%E A183555 Terms a(9) - a(12) computed by _D. S. McNeil_, Dec 28 2010.