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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

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
Offset: 1

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Author

Colin Linzer, Mar 29 2024

Keywords

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 to 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
a(n) != A371626(n);
A371625(n) != y(n);
a(n) != n-f(n/phi) xor A371626(n) != n-f(n/phi);
A371625(n) != f(n/phi) xor y(n) != f(n/phi).

Examples

			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), A371625 (with phi).

Extensions

Elements referring to sequences that were not submitted removed by Peter Munn, Aug 04 2025

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