A393607 Rectangular array R read by descending antidiagonals: row n shows primes p such that (p mod n) = n-1.

2, 3, 3, 5, 5, 2, 7, 7, 5, 3, 11, 11, 11, 7, 19, 13, 13, 17, 11, 29, 5, 17, 17, 23, 19, 59, 11, 13, 19, 19, 29, 23, 79, 17, 41, 7, 23, 23, 41, 31, 89, 23, 83, 23, 17, 29, 29, 47, 43, 109, 29, 97, 31, 53, 19, 31, 31, 53, 47, 139, 41, 139, 47, 71, 29, 43, 37

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Example

Corner:
     2   3   5   7  11  13  17  19  23  29  31
     3   5   7  11  13  17  19  23  29  31  37
     2   5  11  17  23  29  41  47  53  59  71
     3   7  11  19  23  31  43  47  59  67  71
    19  29  59  79  89 109 139 149 179 199 229
     5  11  17  23  29  41  47  53  59  71  83
    13  41  83  97 139 167 181 223 251 293 307
     7  23  31  47  71  79 103 127 151 167 191
    17  53  71  89 107 179 197 233 251 269 359
    19  29  59  79  89 109 139 149 179 199 229
    43 109 131 197 241 263 307 373 439 461 571
    11  23  47  59  71  83 107 131 167 179 191
   103 181 233 311 337 389 467 571 701 727 857
    13  41  83  97 139 167 181 223 251 293 307
For m=3, the primes p such that p (mod 3) = 2 are 2,5,11,17,23,29,41,..., as in row 3.

Mathematica

t = Prime[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, A038700 (column 1), A393606.

Sequence in context: A265145 A103310 A046146 * A081768 A387384 A273493

Adjacent sequences: A393604 A393605 A393606 * A393608 A393609 A393610

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 24 2026

Status

approved