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%I #15 Apr 24 2015 10:56:31
%S 6,7,21,9,15,27,33,11,77,35,45,51,17,153,57,63,75,65,105,87,93,111,
%T 117,135,141,47,423,171,177,183,195,143,231,161,23,437,285,155,185,
%U 215,245,203,261,201,237,243,255,267,273,287,41,861,297,275,315,321,107
%N a(1) = 6; a(2) = 7; for n > 2, a(n) is the smallest number of the form prime + 4 not already used which shares a factor with a(n-1).
%C Analog of EKG-sequence (A064413) on the numbers of the form prime + 4.
%C Conjecture: the sequence {a(n)-4} is a permutation of primes (A000040).
%H Peter J. C. Moses, <a href="/A257312/b257312.txt">Table of n, a(n) for n = 1..1000</a>
%t f[n_] := Block[{o = 2^2, 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@ 57 (* _Michael De Vlieger_, Apr 20 2015 *)
%Y Cf. A000040, A064413, A257311, A257313, A257314, A257315.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Apr 20 2015
%E More terms from _Peter J. C. Moses_, Apr 20 2015
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