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

32, 48, 56, 60, 62, 63, 129, 130, 131, 132, 134, 135, 136, 140, 142, 143, 144, 152, 156, 158, 159, 160, 176, 184, 188, 190, 191, 193, 194, 195, 196, 198, 199, 200, 204, 206, 207, 208, 216, 220, 222, 223, 225, 226, 227, 228, 230, 231, 232, 236, 238, 239, 241

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

David A. Corneth, n, a(n) and the binary balanced expansion of a(n) for n = 1..10000

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A319914 A167527 A114406 * A114416 A046304 A114447

Adjacent sequences: A271781 A271782 A271783 * A271785 A271786 A271787

Keyword

nonn,base

Author

Vladimir Shevelev, Apr 14 2016

Extensions

More terms from Peter J. C. Moses, Apr 14 2016

Status

approved