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A057923 a(0)=0, a(1)=2, a(n) = smallest number such that sequence b(n) = {a(n-1) BITWISE OR a(n)} is strictly monotonically increasing.

%I A057923 #9 Aug 13 2017 16:25:55
%S A057923 0,2,1,4,2,5,8,6,9,16,10,17,12,18,13,32,14,33,16,34,17,36,18,37,24,38,
%T A057923 25,64,26,65,28,66,29,96,30,97,128,98,129,100,130,101,136,102,137,112,
%U A057923 138,113,140,114,141,256,142,257,144,258,145,260,146,261,152,262,153
%N A057923 a(0)=0, a(1)=2, a(n) = smallest number such that sequence b(n) = {a(n-1) BITWISE OR a(n)} is strictly monotonically increasing.
%C A057923 Conjecture: a(n+2) > a(n). - _Robert Israel_, Aug 13 2017
%H A057923 Robert Israel, <a href="/A057923/b057923.txt">Table of n, a(n) for n = 0..10000</a>
%e A057923 See example in A051145.
%p A057923 A[0]:= 0: A[1]:= 2: B[1]:= 2:
%p A057923 for n from 2 to 100 do
%p A057923   for k from B[n-1]-A[n-1] do
%p A057923     b:= Bits:-Or(A[n-1],k);
%p A057923     if b > B[n-1] then A[n]:= k; B[n]:= b; break fi
%p A057923   od
%p A057923 od:
%p A057923 seq(A[i],i=0..100); # _Robert Israel_, Aug 13 2017
%Y A057923 Cf. A051145, A057924, A057925.
%K A057923 easy,nonn,look
%O A057923 0,2
%A A057923 Larry Reeves (larryr(AT)acm.org), Oct 03 2000