

A286326


Least possible maximum of the two initial terms of a Fibonaccilike 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
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OFFSET

0,5


COMMENTS

A Fibonaccilike 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 Fibonaccilike 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 Fibonaccilike 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 Fibonaccilike 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



