login
A333201
Rectangular array read by antidiagonals: row n shows the numbers k such that p(k) = prime(k-1) + 2n, where prime(k) = k-th prime, with 1 prefixed to row 1.
2
1, 2, 5, 3, 7, 10, 4, 9, 12, 25, 6, 13, 16, 73, 35, 8, 15, 17, 78, 43, 47, 11, 20, 19, 80, 54, 48, 31, 14, 23, 22, 88, 62, 92, 63, 283, 18, 26, 24, 93, 69, 98, 67, 296, 100, 21, 28, 33, 95, 81, 115, 138, 320, 181, 155, 27, 30, 37, 125, 83, 122, 147, 332, 206
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. Row 1: A107770, except for initial 1,2.
EXAMPLE
Northwest corner:
1 2 3 4 6 8 11 14 18 21
5 7 9 13 15 20 23 26 28 30
10 12 16 17 19 22 24 33 37 38
25 73 78 80 88 93 95 125 127 129
35 43 54 62 69 81 83 102 107 116
MATHEMATICA
z = 2700; p = Prime[Range[z]];
r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
TableForm[Table[Prime[r[n]], {n, 1, 18}]] (* A333200, array *)
TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 11 2020
STATUS
approved