A336364 Rectangular array by antidiagonals: row n shows the positive integers whose distance to the nearest prime is n.

2, 3, 1, 5, 4, 9, 7, 6, 15, 26, 11, 8, 21, 34, 93, 13, 10, 25, 50, 117, 118, 17, 12, 27, 56, 123, 122, 119, 19, 14, 33, 64, 143, 144, 121, 120, 23, 16, 35, 76, 145, 186, 205, 300, 531, 29, 18, 39, 86, 185, 204, 217, 324, 533, 532, 31, 20, 45, 92, 187, 206

Offset: 1

Author

Clark Kimberling, Jul 19 2020

Keywords

• nonn
• tabl

Comments

Row 1: the primes, A000040. Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive 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
   9  15  21  25  27   33   35   39   45   49   51   55
  26  34  50  56  64   76   86   92   94  116  124  134
  93 117 123 143 145  185  187  203  207  215  219  245
		

Links

• Sean A. Irvine, Java program (github).
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000040, A051699, A336365.

Programs

Mathematica

a[?PrimeQ] = 0; a[n] := Min[NextPrime[n] - n, n - NextPrime[n, -1]];
t = Table[a[n], {n, 1, 2000}]; (* A051699 *)
r[n_] := Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];
TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}]] (* A337364, array *)
Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten    (* A337364, sequence *)