cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Indrani Das

Indrani Das's wiki page.

Indrani Das has authored 2 sequences.

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

Original entry on oeis.org

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

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.
		

Crossrefs

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

A246558 Product of the digits of the n-th Fibonacci number.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 3, 2, 12, 25, 72, 16, 18, 147, 0, 504, 315, 320, 32, 1260, 0, 49, 3360, 3456, 0, 162, 1728, 168, 720, 0, 7776, 0, 33600, 0, 30240, 0, 15680, 0, 311040, 0, 0, 326592, 435456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102060, 3951360, 24883200, 1411200
Offset: 0

Author

Indrani Das, Nov 12 2014

Keywords

Comments

a(n) > 0 iff n in A076564.
Probably, the last nonzero term is a(184). - Giovanni Resta, Jul 14 2015

Examples

			Fibonacci(7) = 13, thus a(7) = 1*3 = 3.
		

Crossrefs

Programs

  • Haskell
    a246558 = a007954 . a000045 -- Reinhard Zumkeller, Nov 17 2014
    
  • Magma
    [0] cat [&*Intseq(Fibonacci(n)): n in [1..100]]; // Vincenzo Librandi, Jan 04 2020
    
  • Mathematica
    Array[Times@@IntegerDigits@Fibonacci[#]&, 100, 0] (* Vincenzo Librandi, Jan 04 2020 *)
  • PARI
    a(n) = if (n, vecprod(digits(fibonacci(n))), 0); \\ Michel Marcus, Feb 11 2025

Formula

a(n) = A007954(A000045(n)). - Reinhard Zumkeller, Nov 17 2014