cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Views

Author

David W. Wilson

Keywords

Links

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

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

Original entry on oeis.org

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

Views

Author

R. Muller

Keywords

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

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

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

Views

Author

David W. Wilson

Keywords

Comments

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

Links

Crossrefs

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).

Programs

  • Magma
    [Seqint(Intseq(8*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Mathematica
    nxt[n_]:=Module[{idn=IntegerDigits[n], idn8=IntegerDigits[8n]}, FromDigits[Join[idn,idn8]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)
  • PARI
    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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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).

Programs

  • Magma
    [Seqint(Intseq(9*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Mathematica
    nxt[n_]:=Module[{idn=IntegerDigits[n], idn9=IntegerDigits[9n]}, FromDigits[Join[idn, idn9]]]; Array[nxt, 100] (* Vincenzo Librandi, Feb 04 2014 *)

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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).

Programs

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

Views

Author

R. Muller

Keywords

Links

Crossrefs

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).

Programs

  • Magma
    [Seqint(Intseq(3*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Maple
    a:=n->n*10^floor(log10(3*n)+1)+3*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018
  • Mathematica
    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

Views

Author

R. Muller

Keywords

Comments

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

Links

Crossrefs

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).

Programs

  • Magma
    [Seqint(Intseq(4*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Maple
    a:=n->n*10^floor(log10(4*n)+1)+4*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018
  • Mathematica
    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 *)
  • PARI
    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

Views

Author

R. Muller

Keywords

Comments

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

Links

Crossrefs

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).

Programs

  • Magma
    [Seqint(Intseq(5*n) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Feb 04 2014
  • Maple
    a:=n->n*10^floor(log10(5*n)+1)+5*n: seq(a(n),n=1..50); # Muniru A Asiru, Jun 23 2018
  • Mathematica
    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 *)
  • PARI
    a(n) = eval(Str(n, 5*n)); \\ Michel Marcus, Sep 21 2015
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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