%I #27 Jul 08 2022 11:52:45

%S 0,1,3,4,19,5,15,25,6,16,21,45,26,7,12,17,41,22,46,27,51,8,56,13,37,

%T 18,42,66,23,47,71,28,52,119,9,33,57,14,148,38,62,19,86,43,67,134,24,

%U 225,48,72,139,29,230,53,254,10,278,34,302,58,259,15,283,39,240,63,197,20,154,288

%N Fibonacci(a(n)) is the least Fibonacci number beginning with n.

%C Fixed points of this sequence are in A038546. - _Alois P. Heinz_, Jul 08 2022

%H T. D. Noe, <a href="/A020344/b020344.txt">Table of n, a(n) for n = 0..10000</a>

%H Ron Knott, <a href="https://r-knott.surrey.ac.uk/Fibonacci/fibmaths.html#section8">Every number starts some Fibonacci Number</a>, The Mathematical Magic of the Fibonacci Numbers.

%F A000045(a(n)) = A020345(n).

%t nn = 100; t = tn = Table[0, {nn}]; found = 0; n = 0; While[found < nn, n++; f = Fibonacci[n]; d = IntegerDigits[f]; i = 1; While[i <= Length[d], k = FromDigits[Take[d, i]]; If[k > nn, Break[]]; If[t[[k]] == 0, t[[k]] = f; tn[[k]] = n; found++]; i++]]; tn = Join[{0}, tn] (* _T. D. Noe_, Apr 02 2014 *)

%o (Python)

%o def aupton(nn):

%o ans, f, g, k = dict(), 0, 1, 0

%o while len(ans) < nn+1:

%o sf = str(f)

%o for i in range(1, len(sf)+1):

%o if int(sf[:i]) > nn:

%o break

%o if sf[:i] not in ans:

%o ans[sf[:i]] = k

%o f, g, k = g, f+g, k+1

%o return [int(ans[str(i)]) for i in range(nn+1)]

%o print(aupton(70)) # _Michael S. Branicky_, Jul 08 2022

%Y Cf. A000045, A020345, A023183, A023184, A038546.

%K nonn,look,base

%O 0,3

%A _David W. Wilson_