A336717 a(n) is the least k such that R(k) = n for some random Fibonacci sequence R (a random Fibonacci sequence R satisfies R(0) = 0, R(1) = 1, and for m > 0, R(m+1) = R(m) + (-1)^r(m) * R(m-1) where r is a sequence of integers).

0, 1, 3, 4, 6, 5, 9, 7, 6, 8, 9, 8, 9, 7, 9, 10, 9, 10, 9, 10, 12, 8, 12, 10, 12, 10, 12, 11, 12, 10, 12, 11, 12, 13, 9, 13, 12, 11, 15, 11, 12, 11, 15, 13, 12, 13, 12, 11, 15, 13, 12, 13, 15, 13, 15, 10, 15, 13, 15, 13, 12, 14, 15, 14, 12, 13, 12, 14, 15, 14

Offset

0,3

Comments

This sequence is well defined as the random Fibonacci sequence A092942 contains every nonnegative integers.

Links

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

James Grime, Random Fibonacci Numbers, Numberphile video (2020).

Rémy Sigrist, C program for A336717

Formula

a(A000045(n)) = n for any n <> 2.

Example

For n = 4:
- random Fibonacci sequences R may start as follows:
  R(0)  R(1)  R(2)  R(3)  R(4)  R(5)  R(6)
  ----  ----  ----  ----  ----  ----  ----
     0     1     1     2     3     5     8
     0     1     1     2     3     5     2
     0     1     1     2     3     1     4
     0     1     1     2     3     1    -2
     0     1     1     2     1     3     4
     0     1     1     2     1     3     2
     0     1     1     2     1    -1     0
     0     1     1     2     1    -1    -2
     0     1     1     0     1     1     2
     0     1     1     0     1     1     0
     0     1     1     0    -1    -1     0
     0     1     1     0    -1    -1    -2
- the value 4 first appears in column R(6),
- so a(4) = 6.

Prog

(C) See Links section.

Crossrefs

Cf. A000045, A092942.

Sequence in context: A083342 A016655 A057757 * A332361 A360655 A058838

Adjacent sequences: A336714 A336715 A336716 * A336718 A336719 A336720

Keyword

nonn

Author

Rémy Sigrist, Aug 01 2020

Status

approved