A246554 - OEIS

%I #38 Sep 08 2022 08:46:09

%S 11,11,22,33,55,88,1313,2121,3434,5555,8989,144144,233233,377377,

%T 610610,987987,15971597,25842584,41814181,67656765,1094610946,

%U 1771117711,2865728657,4636846368,7502575025,121393121393,196418196418,317811317811,514229514229

%N Concatenation of the n-th Fibonacci number with itself.

%C a(n) is the n-th Fibonacci number concatenated with itself; concatenation A000045.

%C 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 Harvey P. Dale, <a href="/A246554/b246554.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000045(n)*(10^A060384(n)+1). - _Robert Israel_, Nov 16 2014

%e The 7th Fibonacci number, 13, is concatenated with itself to become a(7) = 1313.

%p A:= proc(n)

%p local f;

%p f:= combinat:-fibonacci(n);

%p (10^length(f)+1)*f;

%p end proc:

%p map(A, [$1..100]); # _Robert Israel_, Nov 16 2014

%p # second Maple program:

%p a:= n-> (p-> parse(cat(p$2)))((<<0|1>, <1|1>>^n)[1, 2]):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 17 2014

%t Table[FromDigits[Join[Flatten[IntegerDigits[{Fibonacci[n], Fibonacci[n]}]]]], {n, 50}] (* _Vincenzo Librandi_, Nov 15 2014 *)

%t #*10^IntegerLength[#]+#&/@Fibonacci[Range[30]] (* _Harvey P. Dale_, Jul 04 2015 *)

%o (PARI) a(n)=(k->eval(Str(k,k)))(fibonacci(n)) \\ _Charles R Greathouse IV_, Nov 15 2014

%o (Magma) [Seqint(Intseq(Fibonacci(n)) cat Intseq(Fibonacci(n))): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2014

%Y Cf. A247337, A247338, A000045, A060384.

%K nonn,base

%O 1,1

%A _Indrani Das_, Nov 14 2014