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A192179 Array determined by distance to next prime, by antidiagonals.

%I A192179 #13 Apr 07 2016 02:27:12
%S A192179 1,2,3,4,5,8,6,9,14,7,10,11,20,13,24,12,15,26,19,32,23,16,17,34,25,48,
%T A192179 31,90,18,21,38,33,54,47,120,89,22,27,44,37,62,53,142,119,118,28,29,
%U A192179 50,43,74,61,184,141,140,117,30,35,56,49,84,73,204,183,182,139,116
%N A192179 Array determined by distance to next prime, by antidiagonals.
%C A192179 Row r :  numbers k such that r = (least positive integer h for which k + h is a prime).
%C A192179 Every positive integer occurs exactly once, so that as a sequence, A192179 is a permutation of the positive integers.
%C A192179 For r>1, the numbers in row r have the parity of r-1; e.g., the numbers in row 2 are odd.
%H A192179 Ivan Neretin, <a href="/A192179/b192179.txt">Table of n, a(n) for n = 1..5050</a>
%e A192179 Northwest corner:
%e A192179 1....2....4....6....10....12
%e A192179 3....5....9....11...15....17
%e A192179 8....14...20...26...34....38
%e A192179 7....13...19...25...33....37
%e A192179 24...32...48...54...62....74
%e A192179 ...
%e A192179 For example, 14 is in row 3 because 14 + 3 is a prime, unlike 14 + 1 and 14 + 2.
%t A192179 z = 5000;  (* z = number of primes used *)
%t A192179 Do[row[x] = Complement[(#1[[1]] &) /@ Cases[({#1 - x, PrimeQ[#1]} &) /@ (Range[z] + x), {_, True}],
%t A192179    Flatten[Array[row, {x - 1}]]], {x, 1, 10}]
%t A192179 TableForm[Array[row, {10}]]    (* A192179 array *)
%t A192179 Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
%t A192179    n}]]   (* A192179 sequence *)
%t A192179 (* _Peter J. C. Moses_, Jun 24 2011 *)
%Y A192179 Cf. A192175, A192176, A192177, A192178.
%K A192179 nonn,tabl
%O A192179 1,2
%A A192179 _Clark Kimberling_, Jun 24 2011