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%I #13 Aug 11 2020 01:25:40
%S 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,
%T 10,12,11,12,13,9,13,12,11,15,11,12,11,15,13,12,13,12,11,15,13,12,13,
%U 15,13,15,10,15,13,15,13,12,14,15,14,12,13,12,14,15,14
%N 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).
%C This sequence is well defined as the random Fibonacci sequence A092942 contains every nonnegative integers.
%H Rémy Sigrist, <a href="/A336717/b336717.txt">Table of n, a(n) for n = 0..10000</a>
%H James Grime, <a href="https://www.numberphile.com/videos/random-fibonacci-numbers">Random Fibonacci Numbers</a>, Numberphile video (2020).
%H Rémy Sigrist, <a href="/A336717/a336717.txt">C program for A336717</a>
%F a(A000045(n)) = n for any n <> 2.
%e For n = 4:
%e - random Fibonacci sequences R may start as follows:
%e R(0) R(1) R(2) R(3) R(4) R(5) R(6)
%e ---- ---- ---- ---- ---- ---- ----
%e 0 1 1 2 3 5 8
%e 0 1 1 2 3 5 2
%e 0 1 1 2 3 1 4
%e 0 1 1 2 3 1 -2
%e 0 1 1 2 1 3 4
%e 0 1 1 2 1 3 2
%e 0 1 1 2 1 -1 0
%e 0 1 1 2 1 -1 -2
%e 0 1 1 0 1 1 2
%e 0 1 1 0 1 1 0
%e 0 1 1 0 -1 -1 0
%e 0 1 1 0 -1 -1 -2
%e - the value 4 first appears in column R(6),
%e - so a(4) = 6.
%o (C) See Links section.
%Y Cf. A000045, A092942.
%K nonn
%O 0,3
%A _Rémy Sigrist_, Aug 01 2020
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