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Beginning with 3, increasing primes such that no two adjacent terms are congruent mod 4.
1

%I #6 Oct 16 2024 08:15:37

%S 3,5,7,13,19,29,31,37,43,53,59,61,67,73,79,89,103,109,127,137,139,149,

%T 151,157,163,173,179,181,191,193,199,229,239,241,251,257,263,269,271,

%U 277,283,293,307,313,331,337,347,349,359,373,379,389,419,421,431,433

%N Beginning with 3, increasing primes such that no two adjacent terms are congruent mod 4.

%F a(2n-1)==3 (mod 4) and a(2n)==1 (mod 4).

%t a[1] = 3; a[n_] := a[n] = Block[{k}, k = a[n - 1] + 2; While[ ! PrimeQ[k], k = k + 4]; Return[k];]; Table[a[n], {n, 100}]

%K nonn,easy

%O 1,1

%A _Giovanni Teofilatto_, Jan 13 2005

%E Edited and extended by _Ray Chandler_, Jan 19 2005