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%I #10 May 13 2015 15:54:35
%S 1,2,3,4,9,8,15,14,5,7,10,21,16,27,20,33,25,11,30,77,6,49,12,35,18,
%T 125,24,55,32,121,26,99,13,66,65,22,169,44,39,64,81,28,45,56,75,98,
%U 135,112,165,128,225,34,105,17,63,68,147,136,189,170,231,40,243,50
%N a(n) = n if n <= 3, otherwise a(n) is the smallest number not already used and relatively prime to a(n-1) such that the set of prime divisors of one of the numbers {a(n-2), a(n)} is a subset of the set of prime divisors of the other.
%C The sequence is an analog of the Yellowstone sequence A098550 with a more stringent condition on neighboriong terms at distance 2. However, we conjecture that, as with A098550, this is a permutation of the positive integers.
%C By definition, every pair of neighboring terms at distance 2 are strictly connected numbers as defined in comment in A257112.
%H Peter J. C. Moses, <a href="/A257862/b257862.txt">Table of n, a(n) for n = 1..2000</a>
%Y Cf. A098550, A257112, A255348.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, May 11 2015
%E More terms from _Peter J. C. Moses_, May 11 2015