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A257315 a(1) = 34; a(2) = 35; for n > 2, a(n) is the smallest number of the form prime + 32 not already used which shares a factor with a(n-1).

%I A257315 #12 Apr 24 2015 10:57:52
%S A257315 34,35,45,39,51,63,49,91,105,55,75,69,93,99,111,37,259,133,171,129,43,
%T A257315 301,189,135,85,115,145,195,141,159,183,61,793,169,273,213,225,205,
%U A257315 255,231,121,363,243,261,303,309,103,1339,325,265,295,315,339,345,369
%N A257315 a(1) = 34; a(2) = 35; for n > 2, a(n) is the smallest number of the form prime + 32 not already used which shares a factor with a(n-1).
%C A257315 Analog of EKG-sequence (A064413) on the numbers of the form prime + 32.
%C A257315 Conjecture: the sequence {a(n)-32} is a permutation of primes (A000040).
%H A257315 Peter J. C. Moses, <a href="/A257315/b257315.txt">Table of n, a(n) for n = 1..1000</a>
%t A257315 f[n_] := Block[{o = 2^5, s, p, k}, s = {o + 2, o + 3}; For[k = 3, k <= n, k++, p = 2; While[GCD[p + o, s[[k - 1]]] == 1 || MemberQ[s, p + o], p = NextPrime@ p]; AppendTo[s, p + o]]; s]; f@ 55 (* _Michael De Vlieger_, Apr 20 2015 *)
%Y A257315 Cf. A000040, A064413, A257411, A257412, A257413, A257414.
%K A257315 nonn
%O A257315 1,1
%A A257315 _Vladimir Shevelev_, Apr 20 2015
%E A257315 More terms from _Peter J. C. Moses_, Apr 20 2015