A019523 Concatenation of Fibonacci(1) through Fibonacci(n).

1, 11, 112, 1123, 11235, 112358, 11235813, 1123581321, 112358132134, 11235813213455, 1123581321345589, 1123581321345589144, 1123581321345589144233, 1123581321345589144233377, 1123581321345589144233377610, 1123581321345589144233377610987

Offset: 1

Author

R. Muller

Keywords

• base
• nonn

Comments

For n<=800, only a(2) and a(4) are primes. - Dmitry Kamenetsky, Feb 25 2009

a(n) has about kn(n+1) digits, where k = log phi/log 100 = 0.10449... - Charles R Greathouse IV, Sep 19 2012

References

• S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..96
• F. Smarandache, Collected Papers, Vol. II
• Eric Weisstein's World of Mathematics, Fibonacci Number
• Eric Weisstein's World of Mathematics, Consecutive Number Sequences
• Eric Weisstein's World of Mathematics, Smarandache Sequences
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A000045, A038399.

Programs

Haskell

a019523 n = read $ concatMap show $ take n $ tail a000045_list :: Integer
-- Reinhard Zumkeller, Mar 01 2014

Magma

[Seqint(Reverse(&cat[Reverse(Intseq(Fibonacci(k))): k in [1..n]])): n in [1..20]]; // Vincenzo Librandi, Dec 18 2016

Mathematica

Table[FromDigits[Flatten[IntegerDigits[Fibonacci[Range[n]]]]], {n,25}] (* G. C. Greubel, Nov 30 2016 *)

Formula

a(n) = a(n-1)*10^A055642(A000045(n)) + A000045(n). - José de Jesús Camacho Medina, Dec 16 2016