A020344 Fibonacci(a(n)) is the least Fibonacci number beginning with n.

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, 18, 42, 66, 23, 47, 71, 28, 52, 119, 9, 33, 57, 14, 148, 38, 62, 19, 86, 43, 67, 134, 24, 225, 48, 72, 139, 29, 230, 53, 254, 10, 278, 34, 302, 58, 259, 15, 283, 39, 240, 63, 197, 20, 154, 288

Offset

0,3

Comments

Fixed points of this sequence are in A038546. - Alois P. Heinz, Jul 08 2022

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Ron Knott, Every number starts some Fibonacci Number, The Mathematical Magic of the Fibonacci Numbers.

Formula

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

Mathematica

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 *)

Prog

(Python)
def aupton(nn):
    ans, f, g, k = dict(), 0, 1, 0
    while len(ans) < nn+1:
        sf = str(f)
        for i in range(1, len(sf)+1):
            if int(sf[:i]) > nn:
                break
            if sf[:i] not in ans:
                ans[sf[:i]] = k
        f, g, k = g, f+g, k+1
    return [int(ans[str(i)]) for i in range(nn+1)]
print(aupton(70)) # Michael S. Branicky, Jul 08 2022

Crossrefs

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

Sequence in context: A222795 A318419 A263968 * A344459 A348349 A248590

Adjacent sequences: A020341 A020342 A020343 * A020345 A020346 A020347

Keyword

nonn,look,base

Author

David W. Wilson

Status

approved