A183556 Positions of the records of the negative integers in A179319; a(n) is the first position in A179319 equal to -n.

1, 3, 37, 71, 681, 1291, 12237, 23183, 219601, 416019, 3940597, 7465175

Offset: 1

Author

Paul D. Hanna, Jan 12 2011

Keywords

• nonn
• more

Comments

The g.f. of A059973 is (x+x^2-2*x^3)/(1-4*x^2-x^4).

Examples

			Define WL(x) and WU(x) to be respectively the characteristic functions of the lower (A000201) and upper (A001950) Wythoff sequences:
* WL(x) = 1 + x + x^3 + x^4 + x^6 + x^8 + x^9 + x^11 +...+ x^[n*phi] +...
* WU(x) = 1 + x^2 + x^5 + x^7 + x^10 + x^13 + x^15 +...+ x^[n*(phi+1)] +...
then the g.f. of A179319 is the product:
* 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 +...
in which it is conjectured that the following holds:
* A179319(A059973(4n-1)-1) = -(2n-1) for n>=1;
* A179319(A059973(4n)-1) = -(2n) for n>=1.
		

Crossrefs

Cf. A183555, A179319, A059973, A183557, A000201, A001950.

Formula

Conjecture: the positions of the records of the negative integers in A179319 are given by:

* a(2n-1) = A059973(4n-1) - 1 for n>=1;

* a(2n) = A059973(4n) - 1 for n>=1.

Extensions

Terms a(10) - a(12) computed by D. S. McNeil, Dec 28 2010.