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A175343 a(1)=1. a(n) = the smallest positive integer not yet occurring in the sequence such that (binary a(n)) OR (binary a(n-1)) is 2^k -1 for some k >=1.

%I A175343 #11 Dec 15 2016 10:42:38
%S A175343 1,2,3,4,7,5,6,9,14,11,12,15,8,23,10,13,18,29,19,28,27,20,31,16,47,17,
%T A175343 30,21,26,37,58,39,24,55,25,22,41,54,43,52,59,36,63,32,95,33,62,35,60,
%U A175343 51,44,83,45,50,61,34,93,38,57,46,49,78,53,42,85,106,87,40,119,56,71
%N A175343 a(1)=1. a(n) = the smallest positive integer not yet occurring in the sequence such that (binary a(n)) OR (binary a(n-1)) is 2^k -1 for some k >=1.
%C A175343 By "(binary a(n)) OR (binary a(n-1))", it is meant: Write a(n) and a(n-1) in binary (with the smallest, and only the smallest, of the two padded with the appropriate number of leading 0's so that both representations are the same number of binary digits long). OR respective binary digits. Here, each pair of respective digits OR'ed should be 1.
%H A175343 Ivan Neretin, <a href="/A175343/b175343.txt">Table of n, a(n) for n = 1..10000</a>
%p A175343 Contribution from _R. J. Mathar_, Oct 09 2010: (Start)
%p A175343 isA000079 := proc(n) if type(n,'even') then nops(numtheory[factorset](n)) = 1 ; else false ; fi ; end proc: read("transforms") ;
%p A175343 A175343 := proc(n) option remember; if n = 1 then 1; else for a from 1 do earl := false; for j from 1 to n-1 do if procname(j) = a then earl := true; break; end if; od ; if not earl then if isA000079(ORnos(a, procname(n-1))+1 ) then return a; end if; end if; end do: end if; end proc:
%p A175343 seq(A175343(n),n=1..80) ; (End)
%Y A175343 A109812
%K A175343 base,nonn
%O A175343 1,2
%A A175343 _Leroy Quet_, Apr 17 2010
%E A175343 More terms from _R. J. Mathar_, Oct 09 2010