login
A333200
Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.
2
2, 3, 11, 5, 17, 29, 7, 23, 37, 97, 13, 41, 53, 367, 149, 19, 47, 59, 397, 191, 211, 31, 71, 67, 409, 251, 223, 127, 43, 83, 79, 457, 293, 479, 307, 1847, 61, 101, 89, 487, 347, 521, 331, 1949, 541, 73, 107, 137, 499, 419, 631, 787, 2129, 1087, 907, 103, 113
OFFSET
1,1
COMMENTS
Every prime occurs exactly once.
Row 1: A001632, except for initial term
Row 2: A046132
Row 3: A031925
Row 4: A031927
Row 5: A031929
Column 1: A006512, beginning with 5,7,13
EXAMPLE
Northwest corner:
2 3 5 7 13 19 31 43 61 73 103
11 17 23 41 47 71 83 101 107 113 131
29 37 53 59 67 79 89 137 157 163 173
97 367 397 409 457 487 499 691 709 727 751
149 191 251 293 347 419 431 557 587 641 701
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 09 2020
STATUS
approved