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 1-2 of 2 results.

A137440 Triangle T(n,m) read by rows: T(m,n) = (1+n*3^m)-th prime.

Original entry on oeis.org

2, 3, 7, 5, 17, 67, 7, 29, 107, 421, 11, 41, 157, 599, 2153, 13, 53, 199, 769, 2791, 9857, 17, 67, 257, 967, 3469, 12203, 41851, 19, 79, 311, 1151, 4129, 14537, 49697, 167623, 23, 97, 367, 1327, 4817, 16871, 57571, 193957, 645581, 29, 107, 421, 1549, 5521
Offset: 1

Views

Author

Roger L. Bagula, Apr 17 2008

Keywords

Comments

Row sums are: {2, 10, 89, 564, 2961, 13682, 58831, 237546, 920611, 3459888, 12685349, ...}
The first 3 columns are essentially A000040, A031377 and A031918. - R. J. Mathar, May 05 2008

Examples

			{2},
{3, 7},
{5, 17, 67},
{7, 29, 107, 421},
{11, 41, 157, 599, 2153},
{13, 53, 199, 769, 2791, 9857},
{17, 67, 257, 967, 3469, 12203, 41851},
{19, 79, 311, 1151, 4129, 14537, 49697, 167623},
{23, 97, 367, 1327, 4817, 16871, 57571, 193957, 645581},
{29, 107, 421, 1549, 5521, 19301, 65699, 220873, 33591, 2412797},
{31, 127, 467, 1741, 6229, 21649, 73867, 247943, 822587, 2702809, 8807899}

Programs

  • Mathematica
    T[n_, m_] := Prime[1 + n*3^m]; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] Table[Apply[Plus, Table[T[n, m], {m, 0, n}]], {n, 0, 10}];

Extensions

Edited by N. J. A. Sloane, May 16 2008

A358028 Primes p = prime(9*t+1) such that the 9 consecutive primes prime(9*t+1) .. prime(9*t+9) arranged in a 3 X 3 array have at least 2 equal sums along the rows, columns or main diagonals.

Original entry on oeis.org

2, 29, 67, 107, 157, 257, 311, 367, 541, 599, 709, 769, 829, 967, 1021, 1549, 1741, 1811, 1879, 1973, 2609, 2677, 3019, 3541, 3677, 4051, 4217, 4271, 4517, 4597, 4663, 4931, 5227, 5303, 5399, 5449, 5623, 5683, 5839, 6079, 6229, 6301, 6361, 6451, 6949, 7253, 7351, 7477, 7537, 7589, 7673
Offset: 1

Views

Author

Saish S. Kambali, Nov 12 2022

Keywords

Comments

Primes are taken in successive blocks of 9 and arranged, for t>=0,
| prime(9*t+1) | prime(9*t+2) | prime(9*t+3) |
| prime(9*t+4) | prime(9*t+5) | prime(9*t+6) |
| prime(9*t+7) | prime(9*t+8) | prime(9*t+9) |
There are 8 lines altogether: 3 rows, 3 columns, and 2 main diagonals.
The sum of the first row is never duplicated since any other line has a greater sum.
The sum of the last row is never duplicated since any other line has a smaller sum.

Examples

			2 is a term since its block of 9 primes is
  | 2  | 3  | 5  |
  | 7  | 11 | 13 |
  | 17 | 19 | 23 |
which has among its lines (3 + 11 + 19) = (17 + 11 + 5).
67 is a term since its block of 9 primes (the 3rd block) is 67..103,
  | 67 | 71 | 73 |
  | 79 | 83 | 89 |
  | 97 | 101| 103|
which has 67+83+103 = 97+83+73.

Crossrefs

Cf. A105093.
Subsequence of A031918 (by definition).

Programs

  • Mathematica
    a = {}
row = {{1, 4, 7}, {2, 5, 8}, {3, 6, 9}};
col = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
dia = {{1, 3}, {5, 5}, {9, 7}};
Duplicates[l_] :=
Block[{i}, i[n_] := (i[n] = n; Unevaluated@Sequence[]); i /@ l]
Do[If[Duplicates[
    Flatten[{Total[Prime[row + 9 n]], Total[Prime[col + 9 n]],
      Total[Prime[dia + 9 n]]}]] != {},
  AppendTo[a, Prime[9 n + 1]]], {n, 0, 110}]
a (* Gerry Martens, Nov 12 2022 *)

Extensions

More terms from Gerry Martens, Nov 12 2022
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.