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A302053 Squares (A000290) analog for nonstandard factorization process based on the sieve of Eratosthenes (A083221).

%I A302053 #14 Apr 15 2018 15:05:53
%S A302053 0,1,4,9,16,25,36,45,49,64,100,105,115,121,144,169,180,189,196,203,
%T A302053 256,265,289,297,341,361,400,420,429,460,469,475,481,484,529,537,576,
%U A302053 585,676,697,720,745,756,765,784,803,812,817,833,841,961,1024,1027,1060,1075,1081,1156,1188,1197,1257,1309,1345,1364,1369,1377,1411,1444
%N A302053 Squares (A000290) analog for nonstandard factorization process based on the sieve of Eratosthenes (A083221).
%C A302053 Indexing starts with zero, with a(0) = 0, to match with the indexing of A000290.
%C A302053 After initial zero, gives the positions of odd terms in A302051.
%C A302053 After initial zero, contains values obtained with A250245(n^2) sorted into ascending order, or in other words, numbers n such that A250246(n) is a square (in A000290).
%C A302053 Numbers n such that for all terms in iteration sequence n, A302044(n), A302044(A302044(n)), A302044(A302044(A302044(n))), ..., applying A302045(n) gives an even number before the sequence settles to 1.
%H A302053 Antti Karttunen, <a href="/A302053/b302053.txt">Table of n, a(n) for n = 0..3283</a>
%H A302053 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%o A302053 (PARI) for(n=0,4096,if(1==A302052(n),print1(n,",")));
%Y A302053 Cf. A000290, A250245, A302051, A302040, A302044, A302045, A302052 (characteristic function).
%Y A302053 Cf. A000302, A001248 (subsequences).
%K A302053 nonn
%O A302053 0,3
%A A302053 _Antti Karttunen_, Mar 31 2018