A019550 -id:A019550 - cp's OEIS frontend

A061085 a(n) = A019550(n) / 3.

4, 8, 12, 16, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646, 680, 714, 748, 782, 816, 850, 884, 918, 952, 986, 1020, 1054, 1088, 1122, 1156, 1190, 1224, 1258, 1292, 1326, 1360, 1394, 1428, 1462, 1496, 1530, 1564, 1598, 1632, 1666

Offset: 1

Amarnath Murthy, Apr 19 2001

			a(8) = 272 = 816/3, where 816 is 8 concatenated with 16.

Amarnath Murthy, Some propositions on Smarandache n2n sequence, Smarandache Notions Journal, Digital Library of Science, p 126
Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, Smarandache Notions Journal, Digital Library of Science, (2000)

Cf. A019550.

cat2 := proc(a,b) dgsb := max(1,ilog10(b)+1) ; a*10^dgsb+b ; end proc:
A019550 := proc(n) cat2(n,2*n) ; end proc:
A061085 := proc(n) A019550(n)/3 ; end proc: seq(A061085(n),n=1..80) ; # R. J. Mathar, Oct 10 2010

Table[FromDigits[Join[IntegerDigits[n],IntegerDigits[2n]]]/3,{n,50}] (* Harvey P. Dale, Aug 18 2012 *)

a(n) = one-third of the number obtained by concatenating n with 2n.

Offset corrected and sequence extended by R. J. Mathar, Oct 10 2010

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

Original entry on oeis.org

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

David W. Wilson

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

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.

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

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

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

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

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

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

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

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

A009470 a(n) is the concatenation of n and 8n.

Original entry on oeis.org

18, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 13104, 14112, 15120, 16128, 17136, 18144, 19152, 20160, 21168, 22176, 23184, 24192, 25200, 26208, 27216, 28224, 29232, 30240, 31248, 32256, 33264, 34272, 35280, 36288, 37296, 38304, 39312

Offset: 1

David W. Wilson

All terms are divisible by 9. - Michel Marcus, Sep 21 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), this sequence (k=8), A009474 (k=9).

[Seqint(Intseq(8*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

nxt[n_]:=Module[{idn=IntegerDigits[n], idn8=IntegerDigits[8n]}, FromDigits[Join[idn,idn8]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)

a(n) = eval(Str(n, 8*n)); \\ Michel Marcus, Sep 21 2015

A009474 a(n) is the concatenation of n and 9n.

Original entry on oeis.org

19, 218, 327, 436, 545, 654, 763, 872, 981, 1090, 1199, 12108, 13117, 14126, 15135, 16144, 17153, 18162, 19171, 20180, 21189, 22198, 23207, 24216, 25225, 26234, 27243, 28252, 29261, 30270, 31279, 32288, 33297, 34306, 35315, 36324, 37333, 38342, 39351

Offset: 1

David W. Wilson

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), this sequence (k=9).

[Seqint(Intseq(9*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

nxt[n_]:=Module[{idn=IntegerDigits[n], idn9=IntegerDigits[9n]}, FromDigits[Join[idn, idn9]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)

A009440 a(n) is the concatenation of n and 6n.

Original entry on oeis.org

16, 212, 318, 424, 530, 636, 742, 848, 954, 1060, 1166, 1272, 1378, 1484, 1590, 1696, 17102, 18108, 19114, 20120, 21126, 22132, 23138, 24144, 25150, 26156, 27162, 28168, 29174, 30180, 31186, 32192, 33198, 34204, 35210, 36216, 37222, 38228, 39234, 40240

Offset: 1

David W. Wilson

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), this sequence (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).

[Seqint(Intseq(6*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

nxt[n_]:=Module[{idn=IntegerDigits[n], idn6=IntegerDigits[6n]}, FromDigits[Join[idn, idn6]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)
Table[n*10^IntegerLength[6n]+6n,{n,40}] (* Harvey P. Dale, Jul 21 2020 *)

A009441 a(n) is the concatenation of n and 7n.

Original entry on oeis.org

17, 214, 321, 428, 535, 642, 749, 856, 963, 1070, 1177, 1284, 1391, 1498, 15105, 16112, 17119, 18126, 19133, 20140, 21147, 22154, 23161, 24168, 25175, 26182, 27189, 28196, 29203, 30210, 31217, 32224, 33231, 34238, 35245, 36252, 37259, 38266, 39273, 40280

Offset: 1

David W. Wilson

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), this sequence (k=7), A009470 (k=8), A009474 (k=9).

[Seqint(Intseq(7*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

nxt[n_]:=Module[{idn=IntegerDigits[n], idn7=IntegerDigits[7n]}, FromDigits[Join[idn, idn7]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)
Table[n*10^IntegerLength[7n]+7n,{n,40}] (* Harvey P. Dale, Aug 02 2024 *)

A019551 a(n) is the concatenation of n and 3n.

Original entry on oeis.org

13, 26, 39, 412, 515, 618, 721, 824, 927, 1030, 1133, 1236, 1339, 1442, 1545, 1648, 1751, 1854, 1957, 2060, 2163, 2266, 2369, 2472, 2575, 2678, 2781, 2884, 2987, 3090, 3193, 3296, 3399, 34102, 35105, 36108

Offset: 1

R. Muller

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.

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), this sequence (k=3), A019552 (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).

[Seqint(Intseq(3*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

a:=n->n*10^floor(log10(3*n)+1)+3*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018

nxt[n_]:=Module[{idn=IntegerDigits[n], idn3=IntegerDigits[3n]}, FromDigits[Join[idn, idn3]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)
Table[n*10^IntegerLength[3n]+3n,{n,40}] (* Harvey P. Dale, Apr 24 2022 *)

A019552 a(n) is the concatenation of n and 4n.

Original entry on oeis.org

14, 28, 312, 416, 520, 624, 728, 832, 936, 1040, 1144, 1248, 1352, 1456, 1560, 1664, 1768, 1872, 1976, 2080, 2184, 2288, 2392, 2496, 25100, 26104, 27108, 28112, 29116, 30120, 31124, 32128, 33132, 34136, 35140, 36144, 37148, 38152, 39156, 40160, 41164

Offset: 1

R. Muller

a(n) is divisible by 4 for n >= 2. - Michel Marcus, Sep 21 2015

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.

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), this sequence (k=4), A019553 (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).

[Seqint(Intseq(4*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

a:=n->n*10^floor(log10(4*n)+1)+4*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018

Table[FromDigits[Join[IntegerDigits[n],IntegerDigits[4n]]],{n,50}] (* Harvey P. Dale, May 11 2011 *)
nxt[n_]:=Module[{idn=IntegerDigits[n], idn4=IntegerDigits[4n]}, FromDigits[Join[idn, idn4]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)

a(n) = eval(Str(n, 4*n)); \\ Michel Marcus, Sep 21 2015

A019553 a(n) is the concatenation of n and 5n.

Original entry on oeis.org

15, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680, 1785, 1890, 1995, 20100, 21105, 22110, 23115, 24120, 25125, 26130, 27135, 28140, 29145, 30150, 31155, 32160, 33165, 34170, 35175, 36180, 37185, 38190, 39195, 40200

Offset: 1

R. Muller

All terms are divisible by 15. - Michel Marcus, Sep 21 2015

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.

Cf. concatenation of n and k*n: A020338 (k=1), A019550 (k=2), A019551 (k=3), A019552 (k=4), this sequence (k=5), A009440 (k=6), A009441 (k=7), A009470 (k=8), A009474 (k=9).

[Seqint(Intseq(5*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014

a:=n->n*10^floor(log10(5*n)+1)+5*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018

n5n[n_]:=Module[{n5=5n},n*10^IntegerLength[n5]+n5]; Array[n5n,40] (* Harvey P. Dale, Apr 08 2012 *)
nxt[n_]:=Module[{idn=IntegerDigits[n], idn5=IntegerDigits[5n]}, FromDigits[Join[idn, idn5]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)

a(n) = eval(Str(n, 5*n)); \\ Michel Marcus, Sep 21 2015

A235497 2n concatenated with n.

Original entry on oeis.org

21, 42, 63, 84, 105, 126, 147, 168, 189, 2010, 2211, 2412, 2613, 2814, 3015, 3216, 3417, 3618, 3819, 4020, 4221, 4422, 4623, 4824, 5025, 5226, 5427, 5628, 5829, 6030, 6231, 6432, 6633, 6834, 7035, 7236, 7437, 7638, 7839, 8040, 8241, 8442, 8643, 8844, 9045

Offset: 1

Vincenzo Librandi, Feb 04 2014

All terms are divisible by 3. - Michel Marcus, Sep 21 2015

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A019550.

[Seqint(Intseq(n) cat Intseq(2*n)): n in [1..50]];

nxt[n_] := Module[{idn = IntegerDigits[n], idn2 = IntegerDigits[2 n]}, FromDigits[Join[idn2, idn]]]; Array[nxt, 50] (* Librandi *)
Table[FromDigits[Join[IntegerDigits[2n], IntegerDigits[n]]], {n, 40}] (* Alonso del Arte, Sep 13 2014 *)

makelist(2*n*10^floor(log(n)/log(10) + 1) + n,n,50); /* Bruno Berselli, Feb 06 2014, using the closed form added from Alois P. Heinz on Feb 05 2014 */

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

a(n) = 2*n*10^floor(log_10(n) + 1) + n.

cp's OEIS Frontend

A061085 a(n) = A019550(n) / 3.

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

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A009470 a(n) is the concatenation of n and 8n.

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A009474 a(n) is the concatenation of n and 9n.

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Magma

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A009440 a(n) is the concatenation of n and 6n.

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Magma

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A009441 a(n) is the concatenation of n and 7n.

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Magma

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A019551 a(n) is the concatenation of n and 3n.

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A019552 a(n) is the concatenation of n and 4n.

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