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Array by distance to nearest prime, by antidiagonals.
5

%I #7 Feb 13 2014 13:17:45

%S 1,2,5,3,7,26,4,9,34,23,6,11,50,37,118,8,13,56,47,122,53,10,15,64,67,

%T 144,89,120,12,17,76,79,186,119,300,409,14,19,86,83,204,121,324,479,

%U 532,16,21,92,93,206,157,530,531,896,293,18,25,94,97,216,173,534,533,898,631,11

%N Array by distance to nearest prime, by antidiagonals.

%C Row 1: numbers k such that k = 1 or k = 2 or (k - 1 or k + 1) is a prime.

%C Row r > 1: numbers k such that k + r or k - r is a prime but k + q and k - q are not, for q = 1, 2, ..., r - 1.

%C Every positive integer occurs exactly once, so that as a sequence, A192178 is a permutation of the positive integers.

%C For r > 1, the numbers in row r have the parity of r - 1; e.g., the numbers in row 2 are odd.

%e Northwest corner:

%e 1....2....3....4....6....8....10

%e 5....7....9....11...13...15...17

%e 26...34...50...56...64...76...86

%e 23...37...47...67...79...83...93

%e 118..122..144..186..204..206..216

%e ...

%e For example, 34 is in row 3 recause its distance to the nearest prime is 3.

%t z = 5000; (* z = number of primes used *)

%t row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - 1] || PrimeQ[#1 + 1] || #1 == 1 || #1 == 2} &, {z}], {_, True}];

%t Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - x] || PrimeQ[#1 + x]} &, {z}], {_, True}], Flatten[Array[row, {x - 1}]]], {x, 2, 10}];

%t TableForm[Array[row, {10}]] (* A192178 array *)

%t Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,

%t n}]] (* A192178 sequence *)

%t (* by _Peter J. C. Moses_, Jun 24 2011 *)

%Y Cf. A192175, A192176, A192177, A192179.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jun 24 2011