A020338 Doublets: base-10 representation is the juxtaposition of two identical strings.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1010, 1111, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2222, 2323, 2424, 2525, 2626, 2727, 2828, 2929, 3030, 3131, 3232, 3333, 3434, 3535, 3636, 3737, 3838, 3939, 4040, 4141, 4242, 4343, 4444, 4545, 4646

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base
• look
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..9999
• Eric Weisstein's World of Mathematics, Concatenation

Crossrefs

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).

Cf. A004216, A056524.

Programs

GAP

Flat(List([1..2],d->List([10^(d-1)..10^d-1],n->(10^d+1)*n))); # Muniru A Asiru, Mar 31 2018

Haskell

a020338 n = read (ns ++ ns) :: Integer  where ns = show n
-- Reinhard Zumkeller, Jun 07 2015

Magma

[Seqint(Intseq(n) cat Intseq(n)): n in [1..46]]; // Bruno Berselli, Mar 20 2013

Maple

seq(seq((10^d+1)*n, n = 10^(d-1)..10^d-1),d=1..3); # Robert Israel, Jan 02 2015

Mathematica

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

PARI

a(n) = eval(Str(n,n)); \\ Michel Marcus, Sep 10 2015

Sage

[int(str(n)+str(n)) for n in range(1,47)] # Danny Rorabaugh, Oct 10 2015

Formula

a(n) = n*10^(A004216(n)+1) + n. - Reinhard Zumkeller, Aug 11 2007

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

a(n) = n || n. (Where "||" denotes "concatenate". See link "Concatenation".) - Halfdan Skjerning, Apr 01 2018