A019550 a(n) is the concatenation of n and 2n.

12, 24, 36, 48, 510, 612, 714, 816, 918, 1020, 1122, 1224, 1326, 1428, 1530, 1632, 1734, 1836, 1938, 2040, 2142, 2244, 2346, 2448, 2550, 2652, 2754, 2856, 2958, 3060, 3162, 3264, 3366, 3468, 3570, 3672, 3774, 3876, 3978, 4080, 4182, 4284, 4386, 4488, 4590

Offset: 1

Author

R. Muller

Keywords

• nonn
• base
• less
• easy

Comments

Concatenation of digits of n and 2*n. - Harvey P. Dale, Sep 13 2011

All terms are divisible by 6. - Robert Israel, Sep 21 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Sylvester Smith, A Set of Conjectures on Smarandache Sequences, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.

Crossrefs

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).

Cf. A235497.

Supersequence of A117304.

Programs

Magma

[Seqint(Intseq(2*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

Maple

seq(n*(10^(1+ilog10(2*n))+2),n=1..100); # Robert Israel, Sep 21 2015

Mathematica

nxt[n_]:=Module[{idn=IntegerDigits[n],idn2=IntegerDigits[2n]}, FromDigits[ Join[ idn,idn2]]]; Array[nxt,40] (* Harvey P. Dale, Sep 13 2011 *)

PARI

a(n) = eval(Str(n, 2*n)); \\ Michel Marcus, Sep 21 2015

Python

def a(n): return int(str(n) + str(2*n))
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Dec 24 2021

Formula

From Robert Israel, Sep 21 2015 (Start)

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.

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)

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Feb 04 2014