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

%I A336364 #17 Jun 20 2025 08:12:24
%S A336364 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,
%T A336364 123,122,119,19,14,33,64,143,144,121,120,23,16,35,76,145,186,205,300,
%U A336364 531,29,18,39,86,185,204,217,324,533,532,31,20,45,92,187,206
%N A336364 Rectangular array by antidiagonals: row n shows the positive integers whose distance to the nearest prime is n.
%C A336364 Row 1: the primes, A000040. Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%H A336364 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a336/A336364.java">Java program</a> (github).
%H A336364 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A336364 Corner:
%e A336364    2   3   5   7  11   13   17   19   23   29   31   37
%e A336364    1   4   6   8  10   12   14   16   18   20   22   24
%e A336364    9  15  21  25  27   33   35   39   45   49   51   55
%e A336364   26  34  50  56  64   76   86   92   94  116  124  134
%e A336364   93 117 123 143 145  185  187  203  207  215  219  245
%t A336364 a[_?PrimeQ] = 0; a[n_] := Min[NextPrime[n] - n, n - NextPrime[n, -1]];
%t A336364 t = Table[a[n], {n, 1, 2000}]; (* A051699 *)
%t A336364 r[n_] := Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];
%t A336364 TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}]] (* A337364, array *)
%t A336364 Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten    (* A337364, sequence *)
%Y A336364 Cf. A000040, A051699, A336365.
%K A336364 nonn,tabl
%O A336364 1,1
%A A336364 _Clark Kimberling_, Jul 19 2020