A393606 - OEIS

%I #7 Mar 02 2026 20:17:01

%S 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,

%T 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,

%U 16,15,34,13,34,15,20,10,14,12,12,17,17,35,15,39,20

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

%e Corner:

%e    1   2   3   4   5   6   7   8   9  10  11  12

%e    2   3   4   5   6   7   8   9  10  11  12  13

%e    1   3   5   7   9  10  13  15  16  17  20  23

%e    2   4   5   8   9  11  14  15  17  19  20  22

%e    8  10  17  22  24  29  34  35  41  46  50  52

%e    3   5   7   9  10  13  15  16  17  20  23  24

%e    6  13  23  25  34  39  42  48  54  62  63  70

%e    4   9  11  15  20  22  27  31  36  39  43  46

%e    7  16  20  24  28  41  45  51  54  57  72  83

%e    8  10  17  22  24  29  34  35  41  46  50  52

%e   14  29  32  45  53  56  63  74  85  89 105 108

%e    5   9  15  17  20  23  28  32  39  41  43  49

%e   27  42  51  64  68  77  91 105 126 129 148 153

%e 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.

%t t = Table[Take[Select[Range[500], Mod[Prime[#], n] == n - 1 &], 20], {n, 1, 20}];

%t Grid[t]  (* array *)

%t v[n_, k_] := t[[n]][[k]];

%t Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* sequence *)

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

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 24 2026