A263400 Smallest index k such that Fibonacci(k) contains Fibonacci(n) as a proper substring in decimal notation.

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, 3867, 1066, 1801, 953, 10392, 6051, 4677, 6092, 7445, 17382, 19526, 27332, 28226, 102495, 84345, 36245, 44281, 102373, 238850, 163880, 308518

Offset

0,1

Links

Chai Wah Wu, Table of n, a(n) for n = 0..54

Example

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

Maple

with(combinat, fibonacci):
printf("%d %d \n", 0, 15):
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 \n", n, k):
      else
      fi:
     od:
    od:
   od:

Mathematica

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 *)

Prog

(Python)
from gmpy2 import fib2, digits
def A263400(n):
    b, a = fib2(n)
    s, m = digits(b), n
    while True:
        a, b, m = b, a+b, m+1
        t = digits(b)
        if b > a and s in t:
            return m # Chai Wah Wu, Oct 27 2015

Crossrefs

Cf. A263393.

Sequence in context: A362409 A097532 A033335 * A240909 A133817 A173447

Adjacent sequences: A263397 A263398 A263399 * A263401 A263402 A263403

Keyword

nonn,base

Author

Michel Lagneau, Oct 17 2015

Extensions

a(31) - a(47) from Michael De Vlieger, Oct 19 2015

Status

approved