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A336365
Rectangular array by antidiagonals: row n shows the nonnegative integers whose distance to the nearest prime is n.
2
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
1,1
COMMENTS
Row 1: the primes, A000040.
Every nonnegative integer occurs exactly once, so that as a sequence, this is a permutation of the nonnegative integers.
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
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
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jul 19 2020
STATUS
approved