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A246554 Concatenation of the n-th Fibonacci number with itself.

%I A246554 #38 Sep 08 2022 08:46:09
%S A246554 11,11,22,33,55,88,1313,2121,3434,5555,8989,144144,233233,377377,
%T A246554 610610,987987,15971597,25842584,41814181,67656765,1094610946,
%U A246554 1771117711,2865728657,4636846368,7502575025,121393121393,196418196418,317811317811,514229514229
%N A246554 Concatenation of the n-th Fibonacci number with itself.
%C A246554 a(n) is the n-th Fibonacci number concatenated with itself; concatenation A000045.
%C A246554 Also, the quotient of a(n) divided by the n-th Fibonacci number is 10^d(n)+1, where d(n) is the number of digits in the n-th Fibonacci number (A060384).
%H A246554 Harvey P. Dale, <a href="/A246554/b246554.txt">Table of n, a(n) for n = 1..1000</a>
%F A246554 a(n) = A000045(n)*(10^A060384(n)+1). - _Robert Israel_, Nov 16 2014
%e A246554 The 7th Fibonacci number, 13, is concatenated with itself to become a(7) = 1313.
%p A246554 A:= proc(n)
%p A246554 local f;
%p A246554 f:= combinat:-fibonacci(n);
%p A246554 (10^length(f)+1)*f;
%p A246554 end proc:
%p A246554 map(A, [$1..100]); # _Robert Israel_, Nov 16 2014
%p A246554 # second Maple program:
%p A246554 a:= n-> (p-> parse(cat(p$2)))((<<0|1>, <1|1>>^n)[1, 2]):
%p A246554 seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 17 2014
%t A246554 Table[FromDigits[Join[Flatten[IntegerDigits[{Fibonacci[n], Fibonacci[n]}]]]], {n, 50}] (* _Vincenzo Librandi_, Nov 15 2014 *)
%t A246554 #*10^IntegerLength[#]+#&/@Fibonacci[Range[30]] (* _Harvey P. Dale_, Jul 04 2015 *)
%o A246554 (PARI) a(n)=(k->eval(Str(k,k)))(fibonacci(n)) \\ _Charles R Greathouse IV_, Nov 15 2014
%o A246554 (Magma) [Seqint(Intseq(Fibonacci(n)) cat Intseq(Fibonacci(n))): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2014
%Y A246554 Cf. A247337, A247338, A000045, A060384.
%K A246554 nonn,base
%O A246554 1,1
%A A246554 _Indrani Das_, Nov 14 2014