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A084408 Triangle read by rows: if n is prime, row n contains the n smallest primes not already used; if n is composite, row n contains the n smallest composite numbers not already used. A permutation of the positive integers.

%I A084408 #7 May 23 2018 16:36:12
%S A084408 1,2,3,5,7,11,4,6,8,9,13,17,19,23,29,10,12,14,15,16,18,31,37,41,43,47,
%T A084408 53,59,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,
%U A084408 48,49,50,51,52,54,61,67,71,73,79,83,89,97,101,103,107,55,56,57,58,60
%N A084408 Triangle read by rows: if n is prime, row n contains the n smallest primes not already used; if n is composite, row n contains the n smallest composite numbers not already used. A permutation of the positive integers.
%H A084408 Ivan Neretin, <a href="/A084408/b084408.txt">Table of n, a(n) for n = 1..8001</a>
%e A084408 1
%e A084408 2 3
%e A084408 5 7 11
%e A084408 4 6 8 9
%e A084408 13 17 19 23 29
%e A084408 10 12 14 15 16 18
%e A084408 ...
%t A084408 a = {1}; Do[a = Join[a, Take[Select[Complement[Range[Prime[PrimePi@Max@a + n]], a], ! (PrimeQ[#] \[Xor] PrimeQ[n]) &], n]], {n, 2, 12}]; a (* _Ivan Neretin_, May 23 2018 *)
%Y A084408 Cf. A084409, A084410, A084411.
%K A084408 nonn,easy,tabl
%O A084408 1,2
%A A084408 _Amarnath Murthy_, Jun 01 2003
%E A084408 Edited and extended by _David Wasserman_, Dec 27 2004