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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.

%I A080471 #19 Jan 21 2023 01:59:34
%S A080471 1,2,3,34,5,610,377,8,89,610,4181,121393,13,144,1597,10946,1597,4181,
%T A080471 1597,832040,21,514229,233,2584,2584,28657,28657,2584,121393,832040,
%U A080471 317811,832040,233,34,3524578,46368,377,46368,121393,832040,4181,514229
%N 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.
%H A080471 Robert Israel, <a href="/A080471/b080471.txt">Table of n, a(n) for n = 1..10000</a>
%p A080471 IsSubList:= proc(T, S)
%p A080471   local i;
%p A080471   if T = [] then return true fi;
%p A080471   if S = [] then return false fi;
%p A080471   i:= ListTools:-Search(T[1],S);
%p A080471   if i = 0 then false else procname(T[2..-1],S[i+1..-1]) fi
%p A080471 end proc:
%p A080471 f:= proc(n) local T,S,k,v;
%p A080471    T:= convert(n,base,10);
%p A080471    for k from 1 do
%p A080471       v:= combinat:-fibonacci(k);
%p A080471       S:= convert(v,base,10);
%p A080471       if IsSubList(T,S) then return v fi
%p A080471    od
%p A080471 end proc:
%p A080471 map(f, [$1..100]); # _Robert Israel_, Mar 10 2020
%t A080471 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 *)
%o A080471 (Python)
%o A080471 def dmo(n, t):
%o A080471     if t < n: return False
%o A080471     while n and t:
%o A080471         if n%10 == t%10:
%o A080471             n //= 10
%o A080471         t //= 10
%o A080471     return n == 0
%o A080471 def fibo(f=1, g=2):
%o A080471     while True: yield f; f, g = g, f+g
%o A080471 def a(n):
%o A080471     return next(f for f in fibo() if dmo(n, f))
%o A080471 print([a(n) for n in range(1, 77)]) # _Michael S. Branicky_, Jan 21 2023
%Y A080471 Cf. A068164, A068165, A080470.
%K A080471 base,nonn
%O A080471 1,2
%A A080471 _Amarnath Murthy_, Mar 07 2003
%E A080471 Corrected and extended by _Ray Chandler_, Oct 11 2003