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a(2k-1) = k-th prime of form 1 mod 4, a(2k) = k-th prime of form 3 mod 4.
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%I #9 Jun 29 2019 16:42:17

%S 5,3,13,7,17,11,29,19,37,23,41,31,53,43,61,47,73,59,89,67,97,71,101,

%T 79,109,83,113,103,137,107,149,127,157,131,173,139,181,151,193,163,

%U 197,167,229,179,233,191,241,199,257,211,269,223,277,227,281,239,293,251,313

%N a(2k-1) = k-th prime of form 1 mod 4, a(2k) = k-th prime of form 3 mod 4.

%C The graph shows the "race" between the two types of primes. - _T. D. Noe_, Nov 15 2006

%H Harvey P. Dale, <a href="/A111744/b111744.txt">Table of n, a(n) for n = 1..10000</a>

%t Module[{nn=100,pr,m1,m3,len},pr=Prime[Range[nn]];m1=Select[pr,Mod[#,4] == 1&];m3=Select[pr,Mod[#,4]==3&];len=Min[Length[m1],Length[m3]];Flatten[ Thread[ {Take[m1,len],Take[m3,len]}]]] (* _Harvey P. Dale_, Jun 29 2019 *)

%K nonn

%O 1,1

%A _Jon Perry_, Nov 19 2005

%E Corrected and extended by Wendy Kalasky (wkk107(AT)psu.edu), Apr 25 2006

%E Corrected by _T. D. Noe_, Nov 15 2006