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%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
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