A080471 a(n) is the smallest Fibonacci number that is obtained by placing digits anywhere in n; a(n) = n if n is a Fibonacci number.

1, 2, 3, 34, 5, 610, 377, 8, 89, 610, 4181, 121393, 13, 144, 1597, 10946, 1597, 4181, 1597, 832040, 21, 514229, 233, 2584, 2584, 28657, 28657, 2584, 121393, 832040, 317811, 832040, 233, 34, 3524578, 46368, 377, 46368, 121393, 832040, 4181, 514229

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

IsSubList:= proc(T, S)
  local i;
  if T = [] then return true fi;
  if S = [] then return false fi;
  i:= ListTools:-Search(T[1], S);
  if i = 0 then false else procname(T[2..-1], S[i+1..-1]) fi
end proc:
f:= proc(n) local T, S, k, v;
   T:= convert(n, base, 10);
   for k from 1 do
      v:= combinat:-fibonacci(k);
      S:= convert(v, base, 10);
      if IsSubList(T, S) then return v fi
   od
end proc:
map(f, [$1..100]); # Robert Israel, Mar 10 2020

Mathematica

a[n_] := Block[{p = RegularExpression[ StringJoin @@ Riffle[ ToString /@ IntegerDigits[ n], ".*"]], f, k=2}, While[! StringContainsQ[ ToString[f = Fibonacci[ k++]], p]]; f]; Array[a, 42] (* Giovanni Resta, Mar 10 2020 *)

Prog

(Python)
def dmo(n, t):
    if t < n: return False
    while n and t:
        if n%10 == t%10:
            n //= 10
        t //= 10
    return n == 0
def fibo(f=1, g=2):
    while True: yield f; f, g = g, f+g
def a(n):
    return next(f for f in fibo() if dmo(n, f))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023

Crossrefs

Cf. A068164, A068165, A080470.

Sequence in context: A083785 A046487 A062922 * A023184 A114229 A032816

Adjacent sequences: A080468 A080469 A080470 * A080472 A080473 A080474

Keyword

base,nonn

Author

Amarnath Murthy, Mar 07 2003

Extensions

Corrected and extended by Ray Chandler, Oct 11 2003

Status

approved