A356222 Array read by antidiagonals upwards where A(n,k) is the position of the k-th appearance of 2n in the sequence of prime gaps A001223. If A001223 does not contain 2n at least k times, set A(n,k) = -1.

2, 4, 3, 9, 6, 5, 24, 11, 8, 7, 34, 72, 15, 12, 10, 46, 42, 77, 16, 14, 13, 30, 47, 53, 79, 18, 19, 17, 282, 62, 91, 61, 87, 21, 22, 20, 99, 295, 66, 97, 68, 92, 23, 25, 26, 154, 180, 319, 137, 114, 80, 94, 32, 27, 28, 189, 259, 205, 331, 146, 121, 82, 124, 36, 29, 33

Offset: 1

Author

Gus Wiseman, Aug 04 2022

Keywords

• nonn
• tabl

Comments

Prime gaps (A001223) are the differences between consecutive prime numbers. They begin: 1, 2, 2, 4, 2, 4, 2, 4, 6, ...

This is a permutation of the positive integers > 1.

Examples

			Array begins:
        k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9
  n=1:   2   3   5   7  10  13  17  20  26
  n=2:   4   6   8  12  14  19  22  25  27
  n=3:   9  11  15  16  18  21  23  32  36
  n=4:  24  72  77  79  87  92  94 124 126
  n=5:  34  42  53  61  68  80  82 101 106
  n=6:  46  47  91  97 114 121 139 168 197
  n=7:  30  62  66 137 146 150 162 223 250
  n=8: 282 295 319 331 335 378 409 445 476
  n=9:  99 180 205 221 274 293 326 368 416
For example, the positions in A001223 of appearances of 2*3 begin: 9, 11, 15, 16, 18, 21, 23, ..., which is row n = 3 (A320701).
		

Crossrefs

The row containing n is A028334(n).

Row n = 1 is A029707.

Row n = 2 is A029709.

Column k = 1 is A038664.

The column containing n is A274121(n).

Column k = 2 is A356221.

The diagonal A(n,n) is A356223.

A001223 lists the prime gaps.

A073491 lists numbers with gapless prime indices.

A356224 counts even divisors with gapless prime indices, complement A356225.

Cf. A066205, A119313, A193829, A287170, A328457, A356226, A356232.

Programs

Mathematica

gapa=Differences[Array[Prime,10000]];
Table[Position[gapa,2*(k-n+1)][[n,1]],{k,6},{n,k}]