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%I #5 Aug 17 2020 06:40:52
%S 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,
%T 123,122,119,19,14,27,64,143,144,121,120,23,16,33,76,145,186,205,300,
%U 531,29,18,35,86,185,204,217,324,533,532,31,20,39,92,187,206
%N Rectangular array by antidiagonals: row n shows the nonnegative integers whose distance to the nearest prime is n.
%C Row 1: the primes, A000040.
%C Every nonnegative integer occurs exactly once, so that as a sequence, this is a permutation of the nonnegative integers.
%e Corner:
%e 2 3 5 7 11 13 17 19 23 29 31 37
%e 1 4 6 8 10 12 14 16 18 20 22 24
%e 0 9 15 21 24 27 33 35 39 45 49 51
%e 26 34 50 56 64 76 86 92 94 116 124 134
%e 93 117 123 143 145 185 187 203 207 215 219 245
%t a[_?PrimeQ] = 0; a[n_] := Min[NextPrime[n] - n, n - NextPrime[n, -1]];
%t t = Table[a[n], {n, 0, 2000}]; (* A051699 *)
%t r[n_] := -1 + Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];
%t TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}]] (* A336365, array *)
%t Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten (* A336365, sequence *)
%Y Cf. A000040, A051699, A336364.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Jul 19 2020