A023184 -id:A023184 - cp's OEIS frontend

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

David W. Wilson

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

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.

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

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 *)

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

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

A020345 Smallest Fibonacci number beginning with n.

Original entry on oeis.org

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

David W. Wilson

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

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

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.

Cf. A000045, A020344, A023183, A023184.

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 *)

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

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

A023183 a(n) = least k such that Fibonacci(k) ends with n, or -1 if there are none.

Original entry on oeis.org

0, 1, 3, 4, 9, 5, 21, 14, 6, 11, 15, 22, 216, 7, 111, 130, 168, 37, 27, 112, 60, 8, 117, 64, 198, 25, 99, 136, 204, 29, 105, 88, 174, 13, 9, 70, 222, 43, 93, 172, 30, 41, 63, 124, 12, 55, 21, 154, 186, 49, 75, 148, 36, 67, 129, 10, 162, 23, 87, 118, 180, 61, 57, 166, 72, 20

Offset: 0

David W. Wilson

It appears that if n is greater than 99 and congruent to 4 or 6 (mod 8) then there is no Fibonacci number ending in that n. - Jason Earls, Jun 19 2004

This is because there is no Fibonacci number == 4 or 6 (mod 8). - Robert Israel, Sep 11 2020

Robert Israel, Table of n, a(n) for n = 0..9999

Cf. A000045, A023184, A020344, A020345.

V:= Array(0..999,-1):
V[0]:= 0: u:= 1: v:= 0:
for n from 1 to 1500 do
  t:= v;
  v:= u+v mod 1000;
  u:= t;
  if V[v] = -1 then V[v]:= n fi;
  if V[v mod 100] = -1 then V[v mod 100] := n fi;
  if V[v mod 10] = -1 then V[v mod 10]:= n fi;
od:
seq(V[i],i=0..999); # Robert Israel, Sep 11 2020

d[n_]:=IntegerDigits[n]; Table[j=0; While[Length[d[Fibonacci[j]]]<(le=Length[y=d[n]]), j++]; i=j; While[Take[d[Fibonacci[i]],-le]!=y,i++]; i,{n,0,65}] (* Jayanta Basu, May 18 2013 *)

from itertools import count
def A023183(n):
    if n < 2: return n
    if n > 99 and n%8 in {4, 6}: return -1
    k, f, g, s = 3, 1, 2, str(n)
    pow10, seen = 10**len(s), set()
    while (f, g) not in seen:
        seen.add((f, g))
        if g%pow10 == n:
            return k
        f, g, k = g, (f+g)%pow10, k+1
    return -1
print([A023183(n) for n in range(66)]) # Michael S. Branicky, Jun 27 2024

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

Formula

A020345 Smallest Fibonacci number beginning with n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Formula

A023183 a(n) = least k such that Fibonacci(k) ends with n, or -1 if there are none.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Python