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a(1) = 10; a(2) = 11; for n > 2, a(n) is the smallest number of the form prime + 8 not already used which shares a factor with a(n-1).
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%I #16 Apr 24 2015 10:56:59

%S 10,11,55,15,21,27,39,13,91,49,105,25,45,51,69,75,81,87,111,37,259,

%T 147,117,135,115,145,165,121,187,231,159,171,19,247,285,175,189,201,

%U 67,469,301,315,205,235,265,325,345,207,219,237,79,1027,429,249,279,31

%N a(1) = 10; a(2) = 11; for n > 2, a(n) is the smallest number of the form prime + 8 not already used which shares a factor with a(n-1).

%C Analog of EKG-sequence (A064413) on the numbers of the form prime + 8.

%C Conjecture: the sequence {a(n)-8} is a permutation of primes (A000040).

%H Peter J. C. Moses, <a href="/A257313/b257313.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_] := Block[{o = 2^3, 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@ 56 (* _Michael De Vlieger_, Apr 20 2015 *)

%Y Cf. A000040, A064413, A257311, A257312, A257314, A257315.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 20 2015

%E More terms from _Peter J. C. Moses_, Apr 20 2015