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

1,1

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.

Links

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

Sean A. Irvine, Java program (github).

Index entries for sequences that are permutations of the natural numbers

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
   9  15  21  24  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

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 *)

Crossrefs

Cf. A000040, A051699, A336365.

Sequence in context: A345012 A345145 A114690 * A294223 A355618 A376414

Adjacent sequences: A336361 A336362 A336363 * A336365 A336366 A336367

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 19 2020

Status

approved