OFFSET
1,4
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),
- a: g(f) = f(0) * f(1),
- A286326: 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 1 contains n).
For any n>0, a(A000045(n)) = 1.
For any n>2, a(A000032(n)) = 2.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A286321
Rémy Sigrist, Scatterplot of the first 100000 terms
Rémy Sigrist, Illustration of the first terms
EXAMPLE
See illustration of the first terms in Links section.
MATHEMATICA
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++]]; First@ DeleteCases[#, 0] &@ Union@ Map[Times @@ #[[1 ;; 2]] &, Select[s, MemberQ[#, n] &]]], {n, 78}] (* Michael De Vlieger, May 10 2017 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, May 07 2017
STATUS
approved