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A271784 Numbers that have exactly five zeros when written in binary balanced system (A270885). 1

%I

%S 32,48,56,60,62,63,129,130,131,132,134,135,136,140,142,143,144,152,

%T 156,158,159,160,176,184,188,190,191,193,194,195,196,198,199,200,204,

%U 206,207,208,216,220,222,223,225,226,227,228,230,231,232,236,238,239,241

%N Numbers that have exactly five zeros when written in binary balanced system (A270885).

%H David A. Corneth, <a href="/A271784/b271784.txt">Table of n, a(n) for n = 1..10000</a>

%H David A. Corneth, <a href="/A271784/a271784.gp.txt">n, a(n) and the binary balanced expansion of a(n) for n = 1..10000</a>

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.

%e 60 = 2^5 + 2^4 + 2^3 + 2^2 = 2^6 - 2^5 + 2^5 - 2^4 + 2^4 - 2^3 + 2^3 - 2^2 = 2^6 - 2^2 = 1000-100_b, so 60 is a term.

%t Select[Range@ 241, Length[Plus @@ {PadRight[#, Length[#] + 1], -PadLeft[#, Length[#] + 1]} &@ IntegerDigits[#, 2] /. k_ /; k != 0 -> Nothing] == 5 &] (* _Michael De Vlieger_, Apr 14 2016 *)

%o (PARI) is(n) = my(b = concat(0,binary(n))) ;for(i = 2, #b, if(b[i]==1, b[i - 1] += 1; b[i] = -1)); #select(x->x==0,b)==5 \\ _David A. Corneth_, Jan 21 2019

%Y Cf. A270885, A270886, A270887, A270888, A271783.

%K nonn,base

%O 1,1

%A _Vladimir Shevelev_, Apr 14 2016

%E More terms from _Peter J. C. Moses_, Apr 14 2016

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Last modified January 26 05:37 EST 2020. Contains 331273 sequences. (Running on oeis4.)