A358028 - OEIS

%I #66 Oct 06 2024 12:24:21

%S 2,29,67,107,157,257,311,367,541,599,709,769,829,967,1021,1549,1741,

%T 1811,1879,1973,2609,2677,3019,3541,3677,4051,4217,4271,4517,4597,

%U 4663,4931,5227,5303,5399,5449,5623,5683,5839,6079,6229,6301,6361,6451,6949,7253,7351,7477,7537,7589,7673

%N 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.

%C Primes are taken in successive blocks of 9 and arranged, for t>=0,

%C    | prime(9*t+1) | prime(9*t+2) | prime(9*t+3)  |

%C    | prime(9*t+4) | prime(9*t+5) | prime(9*t+6)  |

%C    | prime(9*t+7) | prime(9*t+8) | prime(9*t+9)  |

%C There are 8 lines altogether: 3 rows, 3 columns, and 2 main diagonals.

%C The sum of the first row is never duplicated since any other line has a greater sum.

%C The sum of the last row is never duplicated since any other line has a smaller sum.

%e 2 is a term since its block of 9 primes is

%e   | 2  | 3  | 5  |

%e   | 7  | 11 | 13 |

%e   | 17 | 19 | 23 |

%e which has among its lines (3 + 11 + 19) = (17 + 11 + 5).

%e 67 is a term since its block of 9 primes (the 3rd block) is 67..103,

%e   | 67 | 71 | 73 |

%e   | 79 | 83 | 89 |

%e   | 97 | 101| 103|

%e which has 67+83+103 = 97+83+73.

%t a = {}

%t row = {{1, 4, 7}, {2, 5, 8}, {3, 6, 9}};

%t col = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

%t dia = {{1, 3}, {5, 5}, {9, 7}};

%t Duplicates[l_] :=

%t Block[{i}, i[n_] := (i[n] = n; Unevaluated@Sequence[]); i /@ l]

%t Do[If[Duplicates[

%t     Flatten[{Total[Prime[row + 9 n]], Total[Prime[col + 9 n]],

%t       Total[Prime[dia + 9 n]]}]] != {},

%t   AppendTo[a, Prime[9 n + 1]]], {n, 0, 110}]

%t a (* _Gerry Martens_, Nov 12 2022 *)

%Y Cf. A105093.

%Y Subsequence of A031918 (by definition).

%K nonn

%O 1,1

%A _Saish S. Kambali_, Nov 12 2022

%E More terms from _Gerry Martens_, Nov 12 2022