A371627 - OEIS

A371627

The x-coordinate of the point where x + y = n, x is an integer and x/y is as close as possible to 1/phi.

0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27

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OFFSET

1,5

COMMENTS

Each term is equal to or one greater than the previous term.

The average run length approaches 1+phi.

a(n) = x = either ceiling or floor of n/phi^2, according as which minimizes abs(x/(n-x) - phi).

The 4 following statements are equivalent for any positive integer n and any function f(x) such that for all real x, x-1<f(x)<x+1 and f(x) is integral:

a(n) != A371626(n);

A371625(n) != A371628(n);

a(n) != n-f(n/phi) xor A371626(n) != n-f(n/phi);

A371625(n) != f(n/phi) xor A371628(n) != f(n/phi).

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n)=n-A371628(n)

EXAMPLE

For n=4, the possibilities are (0,4), (1,3), (2,2), and (3,1). 1/3 is the closest to 1/phi out of them so a(4)=1

CROSSREFS

Cf. A094214 (1/phi), A371628 (y_coordinate), A371625 (with phi), A371629 (with -1/phi).