A336364 - OEIS

A336364

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

%I #14 Sep 05 2020 00:28:18

%S 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 123,122,119,19,14,33,64,143,144,121,120,23,16,35,76,145,186,205,300,

%U 531,29,18,39,86,185,204,217,324,533,532,31,20,45,92,187,206

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

%C 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 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a336/A336364.java">Java program</a> (github).

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%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 9 15 21 24 27 33 35 39 45 49 51 55

%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, 1, 2000}]; (* A051699 *)

%t r[n_] := Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];

%t TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}] (* A337364, array *)

%t Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten (* A337364, sequence *)

%Y Cf. A000040, A051699, A336365.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jul 19 2020