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
Examples
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
Programs
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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 *)
Comments