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%I #10 Oct 26 2015 22:28:17
%S 610,13,13,21,13,55,89,121393,121393,1346269,102334155,27777890035288,
%T 14472334024676221,102334155,1725375039079340637797070384,
%U 10610209857723,591286729879,31428600503229159751339745276442091208977285345179605163923475056141186
%N Smallest Fibonacci number containing Fibonacci(n) as a proper substring in decimal notation.
%C The corresponding indices of the Fibonacci numbers are 15, 7, 7, 8, 7, 10, 11, 26, 26, 31, 40, 66, 79, 40, 132, 64, 58, 339, 433, 387, 254, 1158, 691, 74, 623, 1450, 3136, ...
%p with(combinat,fibonacci):
%p printf("%d %d %d \n",0,15,610):
%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 %d \n",n,k,fk):
%p else
%p fi:
%p od:
%p od:
%p od:
%p # alternative:
%p N:= 20000: # get all entries before the first > F(N)
%p for n from 0 to N do
%p S[n]:= sprintf("%d",combinat:-fibonacci(n))
%p od:
%p for n from 0 do
%p for j from n+1 to N do
%p if StringTools:-Search(S[n],S[j]) > 0 then
%p A[n]:= combinat:-fibonacci(j);
%p break
%p fi;
%p od:
%p if not assigned(A[n]) then break fi;
%p od:
%p A[1]:= A[2]:
%p seq(A[i],i=0..n-1); # _Robert Israel_, Oct 16 2015
%Y Cf. A000045.
%K nonn,base
%O 0,1
%A _Michel Lagneau_, Oct 16 2015
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