A263400 - OEIS

%I #21 Oct 31 2015 00:36:25

%S 15,7,7,8,7,10,11,26,26,31,40,66,79,40,132,64,58,339,433,387,254,1158,

%T 691,74,623,1450,3136,3867,1066,1801,953,10392,6051,4677,6092,7445,

%U 17382,19526,27332,28226,102495,84345,36245,44281,102373,238850,163880,308518

%N Smallest index k such that Fibonacci(k) contains Fibonacci(n) as a proper substring in decimal notation.

%H Chai Wah Wu, <a href="/A263400/b263400.txt">Table of n, a(n) for n = 0..54</a>

%e a(7) = 26 because Fibonacci(26) = 121393 contains Fibonacci(7) = 13.

%p with(combinat,fibonacci):

%p printf("%d %d \n",0,15):

%p for n from 1 to 26 do:

%p ii:=0:fn:=fibonacci(n):l:=length(fn) :

%p   for k from 1 to 10000 while(ii=0) do:

%p    fk:=fibonacci(k):xk:=convert(fk,base,10):nk:=nops(xk):

%p    n1:=nk-l+1:

%p     for j from 1 to n1 while(ii=0) do:

%p      s:=sum('xk[j+i-1]*10^(i-1)', 'i'=1..l):

%p       if s=fn and fn<>fk

%p       then

%p       ii:=1:printf("%d %d \n",n,k):

%p       else

%p       fi:

%p      od:

%p     od:

%p    od:

%t Table[k = 1; While[Nand[StringContainsQ[ToString@ Fibonacci@ k, ToString@ Fibonacci@ n], Fibonacci@ k != Fibonacci@ n], k++]; k, {n, 0, 38}] (* _Michael De Vlieger_, Oct 19 2015 *)

%o (Python)

%o from gmpy2 import fib2, digits

%o def A263400(n):

%o     b, a = fib2(n)

%o     s, m = digits(b), n

%o     while True:

%o         a, b, m = b, a+b, m+1

%o         t = digits(b)

%o         if b > a and s in t:

%o             return m # _Chai Wah Wu_, Oct 27 2015

%Y Cf. A263393.

%K nonn,base

%O 0,1

%A _Michel Lagneau_, Oct 17 2015

%E a(31) - a(47) from _Michael De Vlieger_, Oct 19 2015