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%I
%S 1,2,4,3,5,6,8,7,11,9,13,10,12,17,19,14,23,15,29,31,16,37,41,18,20,21,
%T 43,47,22,24,53,59,25,61,26,67,27,71,73,28,79,30,83,32,33,89,97,101,
%U 103,34,35,107,36,109,38,113,39,127,40,42
%N Rearrangement of positive integers according to parity of (prime(n)-1)/2 (see comments).
%C a(1)=1, for n>1: if (prime(n)-1)/2 is odd/even then a(n) is the next prime/composite number.
%t p=Prime[Range[100]];s=Complement[Range[100], p]; bb={1};is=1;ip=0;Do[If[EvenQ[(Prime[i]-1)/2], is=is+1;bb=Append[bb, s[[is]]], ip=ip+1;bb=Append[bb, p[[ip]]]], {i, 2, 60}];bb
%Y Cf. A105365.
%K nonn
%O 1,2
%A _Zak Seidov_, Apr 01 2005
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