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

11, 11, 22, 33, 55, 88, 1313, 2121, 3434, 5555, 8989, 144144, 233233, 377377, 610610, 987987, 15971597, 25842584, 41814181, 67656765, 1094610946, 1771117711, 2865728657, 4636846368, 7502575025, 121393121393, 196418196418, 317811317811, 514229514229

Offset: 1

Author

Indrani Das, Nov 14 2014

Keywords

• nonn
• base

Comments

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

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).

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A247337, A247338, A000045, A060384.

Programs

Magma

[Seqint(Intseq(Fibonacci(n)) cat Intseq(Fibonacci(n))): n in [1..30]]; // Vincenzo Librandi, Nov 15 2014

Maple

A:= proc(n)
local f;
f:= combinat:-fibonacci(n);
(10^length(f)+1)*f;
end proc:
map(A, [$1..100]); # Robert Israel, Nov 16 2014
# second Maple program:
a:= n-> (p-> parse(cat(p$2)))((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 17 2014

Mathematica

Table[FromDigits[Join[Flatten[IntegerDigits[{Fibonacci[n], Fibonacci[n]}]]]], {n, 50}] (* Vincenzo Librandi, Nov 15 2014 *)
#*10^IntegerLength[#]+#&/@Fibonacci[Range[30]] (* Harvey P. Dale, Jul 04 2015 *)

PARI

a(n)=(k->eval(Str(k,k)))(fibonacci(n)) \\ Charles R Greathouse IV, Nov 15 2014

Formula

a(n) = A000045(n)*(10^A060384(n)+1). - Robert Israel, Nov 16 2014