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%I #17 Jan 02 2023 12:30:47
%S 2,6,14,18,38,42,86,90,98,102,206,210,422,426,434,438,878,882,1766,
%T 1770,1778,1782,3566,3570,7142,7146,7154,7158,14318,14322,28646,28650,
%U 28658,28662,57326,57330,114662,114666,114674,114678,229358,229362,229400
%N a(1)=2. For n >=2, a(n) = the least integer >= a(n-1) that is not coprime to both a(n-1)+1 and a(n-1).
%C Also: a(n+1) = a(n)+1 + least prime factor of (a(n)+1), according to an observation by Peter Pein, proved by _M. F. Hasler_, cf. link. - _M. F. Hasler_, Feb 09 2009
%H Peter Pein and M. F. Hasler: <a href="http://list.seqfan.eu/oldermail/seqfan/2009-February/000818.html">Post to the SeqFan list</a>, Feb 09 2009 [From _M. F. Hasler_, Feb 09 2009]
%t a = {2}; Do[ i = a[ [ -1 ] ] + 1; While[ Min[ GCD[ a[ [ -1 ] ], i ], GCD[ a[ [ -1 ] ] + 1, i ] ] == 1, i++ ]; AppendTo[ a, i ], {40} ]; a (* _Stefan Steinerberger_, Aug 04 2008 *)
%o (PARI) print1(a=2); for(i=2,99, print1(","a+=1+factor(a+1)[1,1])) \\ _M. F. Hasler_, Feb 09 2009
%Y Equals A144751 - 1.
%K nonn
%O 1,1
%A _Leroy Quet_, Jul 02 2008
%E More terms from _Stefan Steinerberger_, Aug 04 2008
%E a(42)-a(43) from _Ray Chandler_, Jun 25 2009
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