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A044075 Numbers k such that the string 3,2 occurs in the base-4 representation of k but not of k-1.

%I A044075 #40 Jan 17 2019 03:59:51
%S A044075 14,30,46,56,62,78,94,110,120,126,142,158,174,184,190,206,222,224,248,
%T A044075 254,270,286,302,312,318,334,350,366,376,382,398,414,430,440,446,462,
%U A044075 478,480,504,510,526,542,558,568,574,590,606
%N A044075 Numbers k such that the string 3,2 occurs in the base-4 representation of k but not of k-1.
%C A044075 Numbers whose base-4 representation ends in 3,2 followed by some number of zeros and includes no other 3,2. - _Franklin T. Adams-Watters_, Dec 04 2006
%C A044075 Not the same as A055039 - see A124169.
%C A044075 A 4-automatic set: membership is determined by comparing the base-4 representation of the number to the regular expression /[012]*(3+([01][012]*)?)*320*/. - _Charles R Greathouse IV_, Feb 11 2012 [corrected by _Pontus von Brömssen_, Jan 12 2019]
%C A044075 Alternatively, numbers whose base-4 representation is in the language generated by the regular expression /([012]|3*[01])*3+20*/. - _Pontus von Brömssen_, Jan 17 2019
%H A044075 R. J. Mathar, <a href="/A044075/b044075.txt">Table of n, a(n) for n = 1..10000</a>
%H A044075 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%p A044075 has32 := proc(n) local shft : shft := n : while shft > 0 do if shft mod 16 = 14 then RETURN(true) ; fi : shft := floor(shft/4) : od : RETURN(false) ; end: isA044075 := proc(n) if has32(n) and not has32(n-1) then return(true): else return(false) : fi : end: n := 1 : a := 1 : while n <= 10000 do while not isA044075(a) do a := a+1 : od : printf("%d %d ",n,a) : a := a+1 : n := n+1 : od : # _R. J. Mathar_, Dec 07 2006
%t A044075 Flatten[Position[Partition[Table[If[MemberQ[Partition[IntegerDigits[n, 4], 2, 1], {3, 2}], 1, 0], {n, 1000}], 2, 1], {0, 1}]] + 1 (* _Vincenzo Librandi_, Aug 19 2015 *)
%K A044075 nonn,base,easy
%O A044075 1,1
%A A044075 _Clark Kimberling_