%I #70 May 01 2024 13:44:03

%S 11,22,33,44,55,66,77,88,99,1010,1111,1212,1313,1414,1515,1616,1717,

%T 1818,1919,2020,2121,2222,2323,2424,2525,2626,2727,2828,2929,3030,

%U 3131,3232,3333,3434,3535,3636,3737,3838,3939,4040,4141,4242,4343,4444,4545,4646

%N Doublets: base-10 representation is the juxtaposition of two identical strings.

%H Reinhard Zumkeller, <a href="/A020338/b020338.txt">Table of n, a(n) for n = 1..9999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Concatenation.html">Concatenation</a>

%F a(n) = n*10^(A004216(n)+1) + n. - _Reinhard Zumkeller_, Aug 11 2007

%F G.f.: 11*x/(1-x)^2 - Sum_{d >= 1} 9*x^(10^d)*(100^d*x-10^d*x-100^d)/(1-x)^2). - _Robert Israel_, Jan 02 2015

%F a(n) = n || n. (Where "||" denotes "concatenate". See link "Concatenation".) - _Halfdan Skjerning_, Apr 01 2018

%p seq(seq((10^d+1)*n, n = 10^(d-1)..10^d-1),d=1..3); # _Robert Israel_, Jan 02 2015

%t nxt[n_]:=Module[{idn=IntegerDigits[n], idn1=IntegerDigits[n]}, FromDigits[Join[idn, idn1]]];Array[nxt, 100] (* _Vincenzo Librandi_, Feb 04 2014 *)

%o (Magma) [Seqint(Intseq(n) cat Intseq(n)): n in [1..46]]; // _Bruno Berselli_, Mar 20 2013

%o (Haskell)

%o a020338 n = read (ns ++ ns) :: Integer where ns = show n

%o -- _Reinhard Zumkeller_, Jun 07 2015

%o (PARI) a(n) = eval(Str(n,n)); \\ _Michel Marcus_, Sep 10 2015

%o (Sage) [int(str(n)+str(n)) for n in range(1,47)] # _Danny Rorabaugh_, Oct 10 2015

%o (GAP) Flat(List([1..2],d->List([10^(d-1)..10^d-1],n->(10^d+1)*n))); # _Muniru A Asiru_, Mar 31 2018

%Y Cf. concatenation of n and k*n: this sequence (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).

%Y Cf. A004216, A056524.

%K nonn,base,look

%O 1,1

%A _David W. Wilson_