A263393 Smallest Fibonacci number containing Fibonacci(n) as a proper substring in decimal notation.

610, 13, 13, 21, 13, 55, 89, 121393, 121393, 1346269, 102334155, 27777890035288, 14472334024676221, 102334155, 1725375039079340637797070384, 10610209857723, 591286729879, 31428600503229159751339745276442091208977285345179605163923475056141186

Offset

0,1

Comments

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, ...

Links

Table of n, a(n) for n=0..17.

Maple

with(combinat, fibonacci):
printf("%d %d %d \n", 0, 15, 610):
for n from 1 to 26 do:
ii:=0:fn:=fibonacci(n):l:=length(fn) :
  for k from 1 to 10000 while(ii=0) do:
   fk:=fibonacci(k):xk:=convert(fk, base, 10):nk:=nops(xk):
   n1:=nk-l+1:
    for j from 1 to n1 while(ii=0) do:
     s:=sum('xk[j+i-1]*10^(i-1)', 'i'=1..l):
      if s=fn and fn<>fk
      then
      ii:=1:printf("%d %d %d \n", n, k, fk):
      else
      fi:
     od:
    od:
   od:
# alternative:
N:= 20000: # get all entries before the first > F(N)
for n from 0 to N do
  S[n]:= sprintf("%d", combinat:-fibonacci(n))
od:
for n from 0 do
  for j from n+1 to N do
     if StringTools:-Search(S[n], S[j]) > 0 then
        A[n]:= combinat:-fibonacci(j);
        break
     fi;
  od:
  if not assigned(A[n]) then break fi;
od:
A[1]:= A[2]:
seq(A[i], i=0..n-1);  # Robert Israel, Oct 16 2015

Crossrefs

Cf. A000045.

Sequence in context: A246880 A027514 A246881 * A137563 A301561 A204487

Adjacent sequences: A263390 A263391 A263392 * A263394 A263395 A263396

Keyword

nonn,base

Author

Michel Lagneau, Oct 16 2015

Status

approved