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, 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

Links

Table of n, a(n) for n=1..57.

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

Cf. A333201, A000040, A001632, A006512.

Sequence in context: A039654 A075240 A347358 * A229607 A137332 A292473

Adjacent sequences: A333197 A333198 A333199 * A333201 A333202 A333203

Keyword

nonn,tabl

Author

Clark Kimberling, May 09 2020

Status

approved