A192175 Array of primes determined by distance to next prime, by antidiagonals.

2, 3, 7, 5, 13, 23, 11, 19, 31, 89, 17, 37, 47, 359, 139, 29, 43, 53, 389, 181, 199, 41, 67, 61, 401, 241, 211, 113, 59, 79, 73, 449, 283, 467, 293, 1831, 71, 97, 83, 479, 337, 509, 317, 1933, 523, 101, 103, 131, 491, 409, 619, 773, 2113, 1069, 887, 107

Offset: 1

Author

Clark Kimberling, Jun 24 2011

Keywords

• nonn
• tabl

Comments

Row 1: primes p such that p+1 or p+2 is a prime.

Row r>1: primes p such that the least h for which p+2h is prime is r.

Rows 1-7: A124588, A023200, A031924, A031926, A031928, A031932, A031924.

Examples

			Northwest corner:
  2.....3.....5.....11....17....29....41
  7.....13....19....37....43....67....79
  23....31....47....53....61....73....83
  89....359...389...401...449...479...491
  139...181...241...283...337...409...421
For example, 31 is in row 3 because 31+2*3 is a prime, unlike 31+2*1 and 31+2*2.  Every prime occurs exactly once.  For each row, it is not known whether it is finite.
		

Crossrefs

Cf. A192176, A192177, A192178, A192179.

Programs

Mathematica

z = 5000; (* z=number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1,
      PrimeQ[1 + Prime[#1]] || PrimeQ[2 + Prime[#1]]} &, {z}], {_, True}];
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[2 x + Prime[#1]]} &, {z}], {_, True}], Flatten[Array[row, {x - 1}]]], {x, 2, 16}]; TableForm[Array[Prime[row[#]] &, {10}]] (* A192175 array *)
Flatten[Table[ Prime[row[k][[n - k + 1]]], {n, 1, 11}, {k, 1, n}]] (* A192175 sequence *)
(* Peter J. C. Moses, Jun 20 2011 *)