A020345 Smallest Fibonacci number beginning with n.

0, 1, 2, 3, 4181, 5, 610, 75025, 8, 987, 10946, 1134903170, 121393, 13, 144, 1597, 165580141, 17711, 1836311903, 196418, 20365011074, 21, 225851433717, 233, 24157817, 2584, 267914296, 27777890035288, 28657, 2971215073, 308061521170129, 317811

Offset

0,3

Comments

The graph of the indices A020344 is much more interesting. - T. D. Noe, Apr 02 2014

a(1382) is the first term with > 1000 digits (1004). - Michael S. Branicky, Jul 08 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 0..1389 (terms 1..400 from T. D. Noe)

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

Formula

a(n) = A000045(A020344(n)).

Example

a(4) = 4181 is a Fibonacci number starting with 4.

Mathematica

nn = 31; 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++]]; t = Join[{0}, t] (* 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]] = f
        f, g, k = g, f+g, k+1
    return [int(ans[str(i)]) for i in range(nn+1)]
print(aupton(31)) # Michael S. Branicky, Jul 08 2022

Crossrefs

Cf. A000045, A020344, A023183, A023184.

Sequence in context: A038104 A290972 A097301 * A341715 A085943 A068661

Adjacent sequences: A020342 A020343 A020344 * A020346 A020347 A020348

Keyword

nonn,base

Author

David W. Wilson

Status

approved