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A286321 Least possible strictly positive product of the two initial terms of a Fibonacci-like sequence containing n. 3
1, 1, 1, 2, 1, 4, 2, 1, 3, 4, 2, 6, 1, 3, 6, 4, 4, 2, 6, 5, 1, 8, 3, 9, 10, 4, 12, 4, 2, 15, 6, 9, 5, 1, 10, 8, 3, 6, 9, 20, 10, 4, 7, 12, 4, 12, 2, 8, 15, 6, 14, 16, 5, 18, 1, 16, 20, 8, 18, 3, 6, 19, 9, 24, 20, 10, 28, 4, 7, 30, 12, 32, 4, 12, 35, 2, 8, 14 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000032, A000045, A249783, A286326, A286327.

Sequence in context: A205395 A243070 A243060 * A118235 A304624 A083653

Adjacent sequences:  A286318 A286319 A286320 * A286322 A286323 A286324

KEYWORD

nonn,look

AUTHOR

Rémy Sigrist, May 07 2017

STATUS

approved

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Last modified February 15 20:49 EST 2019. Contains 320138 sequences. (Running on oeis4.)