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

1,1

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.

Links

Table of n, a(n) for n=1..56.

Example

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 not known whether it is finite.

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 *)
(* by Peter J. C. Moses, Jun 20 2011 *)

Crossrefs

Cf. A192176, A192177, A192178, A192179.

Sequence in context: A050367 A354201 A332210 * A294205 A059459 A124440

Adjacent sequences: A192172 A192173 A192174 * A192176 A192177 A192178

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 24 2011

Status

approved