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

0, 15, 159, 303, 2887, 5471, 51839, 98207, 930247, 1762287, 16692639, 31622991

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..12.

Formula

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

* a(2n-1) = A059973(4n+1) - 2 for n>1, with a(1) = 0;

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

Example

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) - 2) = 2n-1 for n>=1;
* A179319(A059973(4n+2) - 2) = 2n for n>=1.

Crossrefs

Cf. A183556, A179319, A059973, A183557, A000201, A001950.

Sequence in context: A300077 A367497 A232414 * A232415 A016297 A206811

Adjacent sequences: A183552 A183553 A183554 * A183556 A183557 A183558

Keyword

nonn,more

Author

Paul D. Hanna, Jan 12 2011

Extensions

Terms a(9) - a(12) computed by D. S. McNeil, Dec 28 2010.

Status

approved