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 1-5 of 5 results.

A245062 Array read by upward antidiagonals: Niven (or Harshad) numbers arranged in rows by their digit sums.

Original entry on oeis.org

1, 2, 10, 3, 20, 100, 4, 12, 110, 1000, 5, 40, 21, 200, 10000, 6, 50, 112, 30, 1010, 100000, 7, 24, 140, 220, 102, 1100, 1000000, 8, 70, 42, 230, 400, 111, 2000, 10000000, 9, 80, 133, 60, 320, 1012, 120, 10010, 100000000, 190, 18, 152, 322, 114, 410, 1120, 201, 10100, 1000000000
Offset: 1

Views

Author

L. Edson Jeffery, Jul 10 2014

Keywords

Comments

The n-th row contains in increasing order all multiples of n with digit sum n.
See A005349 for definitions and references.

Examples

			Array begins as:
  1  10  100  1000  10000  100000  1000000  10000000  100000000  1000000000
  2  20  110   200   1010    1100     2000     10010      10100       11000
  3  12   21    30    102     111      120       201        210         300
  4  40  112   220    400    1012     1120      1300       2020        2200
  5  50  140   230    320     410      500      1040       1130        1220
  6  24   42    60    114     132      150       204        222         240
  7  70  133   322    511     700     1015      1141       1204        1330
  8  80  152   224    440     512      800      1016       1160        1232
  9  18   27    36     45      54       63        72         81          90
190 280  370   460    550     640      730       820        910        1090

Links

Crossrefs

Cf. A002998 (column 1), A245065 (column 2).
Cf. A011557 (row 1), A069537 (row 2), A052217 (row 3), A063997 (row 4), A069540 (row 5), A062768 (row 6), A063416 (row 7), A069543 (row 8), A052223 (row 9).
Cf. A082260 (main diagonal).
Cf. A007953, A005349 (Niven or Harshad numbers).
Cf. A082259.

A082259 Triangle read by rows in which the n-th row contains n multiples of n with digit sum n.

Original entry on oeis.org

1, 2, 20, 3, 12, 21, 4, 40, 112, 220, 5, 50, 140, 230, 320, 6, 24, 42, 60, 114, 132, 7, 70, 133, 322, 511, 700, 1015, 8, 80, 152, 224, 440, 512, 800, 1016, 9, 18, 27, 36, 45, 54, 63, 72, 81, 190, 280, 370, 460, 550, 640, 730, 820, 910, 1090, 209, 308, 407, 506, 605, 704, 803, 902, 2090, 3080, 4070
Offset: 1

Views

Author

Amarnath Murthy, Apr 12 2003

Keywords

Examples

			Triangle begins:
1
2, 20;
3, 12,  21;
4, 40, 112, 220;
5, 50, 140, 230, 320;
6, 24,  42,  60, 114, 132;
7, 70, 133, 322, 511, 700, 1015;
8, 80, 152, 224, 440, 512,  800, 1016;
9, 18,  27,  36,  45,  54,   63,   72,  81;

Links

Crossrefs

Cf. A082260, A082261, A082262, A082263, A002998.

Programs

  • Mathematica
    Table[Take[Select[n Range[10000],Total[IntegerDigits[#]]==n&],n],{n,20}] // Flatten (* Harvey P. Dale, Sep 16 2019 *)

Extensions

Corrected by Anne Donovan, May 29 2003
Corrected and extended by David Wasserman, Aug 26 2004

A082262 Average of row n of A082259.

Original entry on oeis.org

1, 11, 12, 94, 149, 63, 394, 404, 45, 604, 1244, 294, 1246, 1391, 705, 2149, 2087, 593, 3466, 8930, 2301, 4927, 7025, 4875, 17809, 15083, 5052, 24850, 26858, 67065, 42979, 56453, 56040, 75400, 152351, 59193, 108631, 228827, 145485, 1366618, 465026
Offset: 1

Views

Author

Amarnath Murthy, Apr 12 2003

Keywords

Crossrefs

Cf. A082259, A082260, A082261, A082263, A002998.

Programs

  • PARI
    a(n) = my(s=0, k=1); for (i=1, n, while (sumdigits(k*n) != n, k++); s += k*n; k++;); s/n; \\ Michel Marcus, Mar 26 2020

Formula

a(n) = A082261(n)/n.

Extensions

Corrected and extended by Ray Chandler, Oct 08 2005

A082261 Row sums in A082259.

Original entry on oeis.org

1, 22, 36, 376, 745, 378, 2758, 3232, 405, 6040, 13684, 3528, 16198, 19474, 10575, 34384, 35479, 10674, 65854, 178600, 48321, 108394, 161575, 117000, 445225, 392158, 136404, 695800, 778882, 2011950, 1332349, 1806496, 1849320, 2563600
Offset: 1

Views

Author

Amarnath Murthy, Apr 12 2003

Keywords

Crossrefs

Cf. A082259, A082260, A082262, A082263, A002998.

Programs

  • Mathematica
    Do[s = t = 0; i = 1; While[t < n, If[Plus @@ IntegerDigits[i*n] == n, t++; s += i*n]; i++ ]; Print[s], {n, 1, 50}] (* Ryan Propper, Jul 16 2005 *)

Extensions

Corrected and extended by Ryan Propper, Jul 16 2005

A082263 Triangle A082259 with row n divided by n.

Original entry on oeis.org

1, 1, 10, 1, 4, 7, 1, 10, 28, 55, 1, 10, 28, 46, 64, 1, 4, 7, 10, 19, 22, 1, 10, 19, 46, 73, 100, 145, 1, 10, 19, 28, 55, 64, 100, 127, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 19, 28, 37, 46, 55, 64, 73, 82, 190, 280, 370, 4, 7, 13, 16, 19, 22, 28, 31, 34, 37
Offset: 1

Views

Author

Amarnath Murthy, Apr 12 2003

Keywords

Examples

			Triangle begins:
1
1 10
1 4 7
1 10 28 55
1 10 28 46 64
1 4 7 10 19 22

Crossrefs

Cf. A082259, A082260, A082261, A082262, A002998.

Extensions

Corrected and extended by Ray Chandler, Oct 08 2005
Showing 1-5 of 5 results.

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