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

1,2

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.

Links

Table of n, a(n) for n=1..52.

Example

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 ...
  ...

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 *)

Crossrefs

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

Sequence in context: A191448 A191447 A191538 * A080649 A130839 A366565

Adjacent sequences: A361873 A361874 A361875 * A361877 A361878 A361879

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 08 2023

Status

approved