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A263393
Smallest Fibonacci number containing Fibonacci(n) as a proper substring in decimal notation.
1
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, ...
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Oct 16 2015
STATUS
approved