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

1,2

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

Formula

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

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      parse(cat(a(n-1), combinat[fibonacci](n))))
    end:
seq(a(n), n=1..16);  # Alois P. Heinz, Apr 06 2026

Mathematica

Table[FromDigits[Flatten[IntegerDigits[Fibonacci[Range[n]]]]], {n, 25}] (* G. C. Greubel, Nov 30 2016 *)
With[{nn=20}, {fibs=Fibonacci[Range[nn]]}, Table[FromDigits[Flatten[IntegerDigits/@Take[fibs, n]]], {n, nn}]] (* Harvey P. Dale, Dec 27 2025 *)

Prog

(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

Crossrefs

Cf. A000045, A038399.

Sequence in context: A383429 A132926 A094704 * A359143 A375101 A361350

Adjacent sequences: A019520 A019521 A019522 * A019524 A019525 A019526

Keyword

base,nonn

Author

R. Muller

Status

approved