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

1,1

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.

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)

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 *)

Prog

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

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.

Sequence in context: A359434 A358693 A371413 * A117304 A022759 A335540

Adjacent sequences: A019547 A019548 A019549 * A019551 A019552 A019553

Keyword

nonn,base,less,easy

Author

R. Muller

Extensions

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

Status

approved