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A185511 Array: row n shows numbers m such that prime(m) is in row n of the natural number array A000027, by antidiagonals.

%I A185511 #4 Mar 30 2012 18:57:17
%S A185511 1,4,2,5,3,6,10,7,11,8,12,9,34,17,13,19,15,44,29,20,18,22,28,80,37,23,
%T A185511 25,14,33,40,95,55,60,67,21,16,43,51,143,85,76,110,31,30,46,47,71,221,
%U A185511 109,194,127,45,41,145,26,59,91,243,155,252,181,61,52,244,38,24,75,103,314,175,349,202,63,72,316,42,32,27
%N A185511 Array:  row n shows numbers m such that prime(m) is in row n of the natural number array A000027, by antidiagonals.
%C A185511 If the conjecture at A185510 is true, then the A185512, as a sequence, is a permutation of the natural numbers.
%e A185511 Start with the natural number array A000027:
%e A185511 1...2...4...7
%e A185511 3...5...8..12
%e A185511 6...9..13..18
%e A185511 (The antidiagonals are 1; 2,3; 4,5,6; 7,8,9,10;...).
%e A185511 Primes, by rows (A185510):
%e A185511 2.....7....11....29... in row 1 of A000027
%e A185511 3.....5....17....23... in row 2
%e A185511 13...31...139...193... in row 3, etc.
%e A185511 Now replace each prime by its index to obtain A185511.
%e A185511 Northwest corner:
%e A185511 1.....4....5...10...12...19...22...33
%e A185511 2.....3....7....9...15...28...40...51
%e A185511 6....11...34...44...80...95..143..221
%e A185511 8....17...29...37...55...85..109..155
%e A185511 13...20...23...60...76..194..252..349
%t A185511 f[n_,k_]:=n+(k+n-2) (k+n-1)/2;
%t A185511 Do[t[n]={};Do[If[PrimeQ[f[n,k]],AppendTo[t[n],f[n,k]]],{k,1,1000}]; t[n];
%t A185511 u[n]={};Do[If[MemberQ[t[n],Prime[m]],AppendTo[u[n],m]],{m,1,1000}],{n,12}]
%t A185511 TableForm[Table[u[n],{n,12}]]
%Y A185511 Cf. A000027, A000040, A185510.
%K A185511 nonn,tabl
%O A185511 1,2
%A A185511 _Clark Kimberling_, Jan 29 2011