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A188529 Numbers which contain only the digit 3 in their base-4 representation, with at most one exception. If the exception is the most-significant digit, it must be the digit 1 or 2, otherwise the exception must be the digit 2.

%I A188529 #9 Nov 14 2014 07:58:03
%S A188529 1,2,3,7,11,14,15,31,47,59,62,63,127,191,239,251,254,255,511,767,959,
%T A188529 1007,1019,1022,1023,2047,3071,3839,4031,4079,4091,4094,4095,8191,
%U A188529 12287,15359,16127,16319,16367,16379,16382,16383,32767,49151,61439,64511,65279,65471,65519
%N A188529 Numbers which contain only the digit 3 in their base-4 representation, with at most one exception. If the exception is the most-significant digit, it must be the digit 1 or 2, otherwise the exception must be the digit 2.
%C A188529 The sequence lists the positive binomial coefficient predictors in base 4. For definition, see paper in link.
%C A188529 A subsequence of A089633.
%H A188529 V. Shevelev, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Shevelev/shevelev14.html">Binomial Coefficient Predictors</a>, Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.8
%e A188529 (767)_10 = (23333)_4 contains only digits 3, with the exception the leading digit which is 2. Therefore 767 is in the sequence.
%e A188529 (4091)_10 = (333323)_4 contains only digits 3, with the exception a digit 2.
%p A188529 isA188529 := proc(n) local dgs ,n3,p,d; dgs := convert(n,base,4); n3 := 0 ; for p from 1 to nops(dgs) do d := op(p,dgs) ; if d <> 3 then n3 := n3+1 ; if n3 >=2 then return false; end if; if p < nops(dgs) and d <> 2 then return false; end if; if p = nops(dgs) and d = 0 then return false; end if; end if; end do: return true; end proc:
%p A188529 A188529 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if isA188529(a) then return a; end if; end do; end if; end proc:
%p A188529 seq(A188529(n),n=1..50) ; # _R. J. Mathar_, Apr 03 2011
%Y A188529 Cf. A024036, A089633, A188341, A188499.
%K A188529 nonn,base
%O A188529 1,2
%A A188529 _Vladimir Shevelev_, Apr 03 2011