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A286326 Least possible maximum of the two initial terms of a Fibonacci-like sequence containing n. 4
0, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 3, 1, 3, 3, 2, 4, 2, 3, 4, 1, 4, 3, 3, 5, 2, 4, 4, 2, 5, 3, 4, 5, 1, 5, 4, 3, 6, 3, 5, 5, 2, 6, 4, 4, 6, 2, 6, 5, 3, 7, 4, 5, 6, 1, 7, 5, 4, 7, 3, 6, 6, 3, 8, 5, 5, 7, 2, 7, 6, 4, 8, 4, 6, 7, 2, 8, 6, 5, 8, 3, 7, 7, 4, 9, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A Fibonacci-like sequence f satisfies f(n+2) = f(n+1) + f(n), and is uniquely identified by its two initial terms f(0) and f(1); here we consider Fibonacci-like sequences with f(0) >= 0 and f(1) >= 0.

This sequence is part of a family of variations of A249783, where we minimize a function g of the initial terms of Fibonacci-like sequences containing n:

- A249783: g(f) = f(0) + f(1),

- A286321: g(f) = f(0) * f(1),

- a:       g(f) = max(f(0), f(1)),

- A286327: g(f) = f(0)^2 + f(1)^2.

For any n>0, a(n) <= n (as the Fibonacci-like sequence with initial terms n and 0 contains n).

For any n>0, a(A000045(n)) = 1.

Apparently the same as A097368 for n > 1. - Georg Fischer, Oct 09 2018

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of the first 100000 terms

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, C program for A286326

Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 1..100000 (where the color is function of the least k > 0 such that a(n)/n >= A000045(k)/A001654(k))

EXAMPLE

See illustration of the first terms in Links section.

MATHEMATICA

{0}~Join~Table[Module[{a = 0, b = 1, s = {}}, While[a <= n, AppendTo[s, Flatten@ NestWhileList[{#2, #1 + #2} & @@ # &, {a, b}, Last@ # < n &]]; If[a + b >= n, a++; b = 1, b++]]; Min@ Map[Max@ #[[1 ;; 2]] &, Select[s, MemberQ[#, n] &]]], {n, 86}] (* Michael De Vlieger, May 10 2017 *)

CROSSREFS

Cf. A000045, A001654, A097368, A249783, A286321, A286327.

Sequence in context: A256660 A109967 A000119 * A097368 A271900 A194083

Adjacent sequences:  A286323 A286324 A286325 * A286327 A286328 A286329

KEYWORD

nonn,look

AUTHOR

Rémy Sigrist, May 07 2017

STATUS

approved

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)