A361876 Dispersion of the odd primes: a rectangular array read by downward antidiagonals.

1, 3, 2, 7, 5, 4, 19, 13, 11, 6, 71, 43, 37, 17, 8, 359, 193, 163, 61, 23, 9, 2423, 1181, 971, 293, 89, 29, 10, 21589, 9547, 7669, 1931, 463, 113, 31, 12, 244481, 99523, 78101, 16699, 3301, 619, 131, 41, 14, 3413801, 1292831, 994559, 184463, 30593, 4583, 743

Offset: 1

Author

Clark Kimberling, Apr 08 2023

Keywords

• nonn
• tabl

Comments

Every positive integer occurs exactly once. As a dispersion, the array is also an interspersion. Column 1 consists of 1, 2, and the composite positive integers. Row 2 is essentially A119533.

Examples

			Corner:
   1     3     7    19    71   359 ...
   2     5    13    43   193  1181 ...
   4    11    37   163   971  7669 ...
   6    17    61   293  1931 16699 ...
   8    23    89   463  3301 30593 ...
   9    29   113   619  4583 44041 ...
  10    31   131   743  5653 55711 ...
  12    41   181  1091  8753 90403 ...
  ...
		

Crossrefs

Cf. A000040, A065091, A114537 (dispersion of the primes), A114577 (dispersion of the composite numbers).

Programs

Mathematica

t = Map[NestWhileList[Prime[1 + #] &, #, # < 20000000 &, 1, Infinity, -1] &,
   Complement[Range[Last[#]], #] &[Prime[Range[2, 1000]]]];
Grid[Take[t, 15]]  (* Peter J. C. Moses, Apr 06 2023 *)