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

1,1

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).

Links

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

Formula

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

Example

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

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 *)

Prog

(PARI) a(n)=(k->eval(Str(k, k)))(fibonacci(n)) \\ Charles R Greathouse IV, Nov 15 2014
(Magma) [Seqint(Intseq(Fibonacci(n)) cat Intseq(Fibonacci(n))): n in [1..30]]; // Vincenzo Librandi, Nov 15 2014

Crossrefs

Cf. A247337, A247338, A000045, A060384.

Sequence in context: A003887 A138844 A022345 * A218163 A152082 A070849

Adjacent sequences: A246551 A246552 A246553 * A246555 A246556 A246557

Keyword

nonn,base

Author

Indrani Das, Nov 14 2014

Status

approved