A257314 - OEIS

A257314

a(1) = 18; a(2) = 19; for n > 2, a(n) is the smallest number of the form prime + 16 not already used which shares a factor with a(n-1).

%I #14 Apr 24 2015 10:57:25

%S 18,19,57,21,27,33,39,45,35,63,69,23,207,75,87,29,435,95,105,77,99,

%T 117,123,129,147,119,153,165,125,155,195,143,209,285,183,189,213,243,

%U 249,83,1079,273,245,215,255,267,89,623,287,329,47,893,323,399,279,297

%N a(1) = 18; a(2) = 19; for n > 2, a(n) is the smallest number of the form prime + 16 not already used which shares a factor with a(n-1).

%C Analog of EKG-sequence (A064413) on the numbers of the form prime + 16.

%C Conjecture: the sequence {a(n)-16} is a permutation of primes (A000040).

%H Peter J. C. Moses, <a href="/A257314/b257314.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_] := Block[{o = 16, 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, A257313, A257315.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 20 2015

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