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%I #25 Feb 27 2020 22:48:32
%S 2,3,5,7,13,11,17,19,29,23,37,31,41,43,53,47,61,59,73,67,89,71,97,79,
%T 101,83,109,103,113,107,137,127,149,131,157,139,173,151,181,163,193,
%U 167,197,179,229,191,233,199,241,211,257,223,269,227,277,239,281,251,293
%N Lexicographically earliest permutation of primes such that for n>1 forms 4*k+1 and 4*k+3 alternate.
%H Reinhard Zumkeller, <a href="/A108546/b108546.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) mod 4 = 3 - 2 * (n mod 2) for n>1.
%F For n > 1: a(n) = A111745(n-1).
%F a(2*n+1) - a(2*n) = A102261(n).
%F From _Antti Karttunen_, Feb 27 2020: (Start)
%F a(1) = 2, a(2n) = A002145(n), a(2n+1) = A002144(n).
%F a(n) = A000040(A332807(n)).
%F (End)
%t terms = 60; A111745 = Module[{prs = Prime[Range[2terms]], m3, m1, min}, m3 = Select[prs, Mod[#, 4] == 3&]; m1 = Select[prs, Mod[#, 4] == 1&]; min = Min[Length[m1], Length[m3]]; Riffle[Take[m3, min], Take[m1, min]]]; a[1] = 2; a[n_] := A111745[[n-1]]; Table[a[n], {n, 1, terms}] (* _Jean-François Alcover_, May 18 2017, using _Harvey P. Dale_'s code for A111745 *)
%o (Haskell)
%o import Data.List (transpose)
%o a108546 n = a108546_list !! (n-1)
%o a108546_list = 2 : concat
%o (transpose [a002145_list, a002144_list])
%o -- _Reinhard Zumkeller_, Nov 13 2014, Feb 22 2011
%o (PARI)
%o up_to = 10000;
%o A108546list(up_to) = { my(v=vector(up_to), p,q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4,up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
%o v108546 = A108546list(up_to);
%o A108546(n) = v108546[n]; \\ _Antti Karttunen_, Feb 27 2020
%Y Cf. A000040, A002144, A002145, A102261, A108547 (fixed points), A108548, A111745, A332806 (inverse), A332807.
%Y Cf. also A267101, A332211.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 10 2005
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