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A122397 a(1)=1, a(2)=2, a(3)=3; for n >= 4, a(n) is the smallest positive integer not occurring earlier in the sequence such that gcd(a(n-2), a(n)) is a prime. 1

%I

%S 1,2,3,4,6,10,8,5,14,15,7,9,21,12,18,22,16,11,26,33,13,24,39,27,30,42,

%T 25,20,35,34,28,17,38,51,19,36,57,46,45,23,40,69,54,48,32,50,58,44,29,

%U 55,87,60,63,62,49,31,56,93,66,72,52,70,65,64,75,74,78,37,68,111,82,81

%N a(1)=1, a(2)=2, a(3)=3; for n >= 4, a(n) is the smallest positive integer not occurring earlier in the sequence such that gcd(a(n-2), a(n)) is a prime.

%C Sequence is probably a permutation of the positive integers.

%t f[s_] := Block[{k = 1}, While[MemberQ[s, k] || ! PrimeQ[GCD[s[[ -2]], k]], k++ ]; Append[s, k] ]; Nest[f, {1, 2, 3}, 70] (* _Ray Chandler_, Sep 05 2006 *)

%Y Cf. A122398.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 31 2006

%E Corrected and extended by _Ray Chandler_, Sep 05 2006

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Last modified April 22 14:33 EDT 2021. Contains 343177 sequences. (Running on oeis4.)