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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. 4
0, 15, 159, 303, 2887, 5471, 51839, 98207, 930247, 1762287, 16692639, 31622991 (list; graph; refs; listen; history; text; internal format)
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: A016849 A300077 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

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Last modified May 25 00:03 EDT 2022. Contains 354047 sequences. (Running on oeis4.)