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

1,1

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.

Links

Table of n, a(n) for n=1..61.

Example

 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

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 *)

Crossrefs

Cf. A000040, A051699, A336364.

Sequence in context: A246186 A246179 A166285 * A002472 A060116 A347120

Adjacent sequences: A336362 A336363 A336364 * A336366 A336367 A336368

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 19 2020

Status

approved