A393606 Rectangular array read by descending antidiagonals: row n shows the indices m such that prime(m) (mod n) = n-1.

1, 2, 2, 3, 3, 1, 4, 4, 3, 2, 5, 5, 5, 4, 8, 6, 6, 7, 5, 10, 3, 7, 7, 9, 8, 17, 5, 6, 8, 8, 10, 9, 22, 7, 13, 4, 9, 9, 13, 11, 24, 9, 23, 9, 7, 10, 10, 15, 14, 29, 10, 25, 11, 16, 8, 11, 11, 16, 15, 34, 13, 34, 15, 20, 10, 14, 12, 12, 17, 17, 35, 15, 39, 20

Offset

1,2

Links

Table of n, a(n) for n=1..74.

Example

Corner:
   1   2   3   4   5   6   7   8   9  10  11  12
   2   3   4   5   6   7   8   9  10  11  12  13
   1   3   5   7   9  10  13  15  16  17  20  23
   2   4   5   8   9  11  14  15  17  19  20  22
   8  10  17  22  24  29  34  35  41  46  50  52
   3   5   7   9  10  13  15  16  17  20  23  24
   6  13  23  25  34  39  42  48  54  62  63  70
   4   9  11  15  20  22  27  31  36  39  43  46
   7  16  20  24  28  41  45  51  54  57  72  83
   8  10  17  22  24  29  34  35  41  46  50  52
  14  29  32  45  53  56  63  74  85  89 105 108
   5   9  15  17  20  23  28  32  39  41  43  49
  27  42  51  64  68  77  91 105 126 129 148 153
For m=3, the primes p such that (p mod 3) = 2 are 2,5,11,17,23,29,41,..., indexed by 1,3,5,7,9,10,13, as in row 3.

Mathematica

t = Table[Take[Select[Range[500], Mod[Prime[#], n] == n - 1 &], 20], {n, 1, 20}];
Grid[t]  (* array *)
v[n_, k_] := t[[n]][[k]];
Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* sequence *)

Crossrefs

Cf. A000040, A219109 (column 1), A393607.

Sequence in context: A116464 A346136 A284532 * A125585 A327236 A191860

Adjacent sequences: A393603 A393604 A393605 * A393607 A393608 A393609

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 24 2026

Status

approved