A336365 Rectangular array by antidiagonals: row n shows the nonnegative integers whose distance to the nearest prime is n.

2, 3, 1, 5, 4, 0, 7, 6, 9, 26, 11, 8, 15, 34, 93, 13, 10, 21, 50, 117, 118, 17, 12, 25, 56, 123, 122, 119, 19, 14, 27, 64, 143, 144, 121, 120, 23, 16, 33, 76, 145, 186, 205, 300, 531, 29, 18, 35, 86, 185, 204, 217, 324, 533, 532, 31, 20, 39, 92, 187, 206

Offset: 1

Author

Clark Kimberling, Jul 19 2020

Keywords

• nonn
• tabl

Comments

Row 1: the primes, A000040.

Every nonnegative integer occurs exactly once, so that as a sequence, this is a permutation of the nonnegative integers.

Examples

			 Corner:
   2    3    5    7   11   13   17   19   23   29   31   37
   1    4    6    8   10   12   14   16   18   20   22   24
   0    9   15   21   24   27   33   35   39   45   49   51
  26   34   50   56   64   76   86   92   94  116  124  134
  93  117  123  143  145  185  187  203  207  215  219  245
		

Crossrefs

Cf. A000040, A051699, A336364.

Programs

Mathematica

a[?PrimeQ] = 0; a[n] := Min[NextPrime[n] - n, n - NextPrime[n, -1]];
t = Table[a[n], {n, 0, 2000}]; (*  A051699 *)
r[n_] := -1 + Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];
TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}]] (* A336365, array *)
Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten  (* A336365, sequence *)