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%I #56 Dec 30 2023 23:43:16
%S 12,24,36,48,510,612,714,816,918,1020,1122,1224,1326,1428,1530,1632,
%T 1734,1836,1938,2040,2142,2244,2346,2448,2550,2652,2754,2856,2958,
%U 3060,3162,3264,3366,3468,3570,3672,3774,3876,3978,4080,4182,4284,4386,4488,4590
%N a(n) is the concatenation of n and 2n.
%C Concatenation of digits of n and 2*n. - _Harvey P. Dale_, Sep 13 2011
%C All terms are divisible by 6. - _Robert Israel_, Sep 21 2015
%H Vincenzo Librandi, <a href="/A019550/b019550.txt">Table of n, a(n) for n = 1..1000</a>
%H Sylvester Smith, <a href="https://www.gallup.unm.edu/~smarandache/SYLSMITH.HTM">A Set of Conjectures on Smarandache Sequences</a>, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
%F From _Robert Israel_, Sep 21 2015 (Start)
%F G.f.: (6*(2*x+75*x^5-60*x^6) + 90*Sum_{k>=1} 10^k*x^(5*10^k)*(5*10^k - (5*10^k-1)*x))/(1-x)^2.
%F a(n+2) - 2*a(n+1) + a(n) = 45*10^(2*k+1) if n = 5*10^k-2, 90*10^k-450*10^(2*k) if n = 5*10^k-1, 0 otherwise. (End)
%p seq(n*(10^(1+ilog10(2*n))+2),n=1..100); # _Robert Israel_, Sep 21 2015
%t nxt[n_]:=Module[{idn=IntegerDigits[n],idn2=IntegerDigits[2n]}, FromDigits[ Join[ idn,idn2]]]; Array[nxt,40] (* _Harvey P. Dale_, Sep 13 2011 *)
%o (Magma) [Seqint(Intseq(2*n) cat Intseq(n)): n in [1..50]]; // _Vincenzo Librandi_, Feb 04 2014
%o (PARI) a(n) = eval(Str(n, 2*n)); \\ _Michel Marcus_, Sep 21 2015
%o (Python)
%o def a(n): return int(str(n) + str(2*n))
%o print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Dec 24 2021
%Y Cf. concatenation of n and k*n: A020338 (k=1), this sequence (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. A235497.
%Y Supersequence of A117304.
%K nonn,base,less,easy
%O 1,1
%A R. Muller
%E Offset changed from 0 to 1 by _Vincenzo Librandi_, Feb 04 2014
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