%I #13 Jan 15 2024 11:03:56

%S 0,1,2,3,4,5,-6,-5,-4,-3,-2,-1,-12,-11,-10,-9,-8,-7,-18,-17,-16,-15,

%T -14,-13,-24,-23,-22,-21,-20,-19,-30,-29,-28,-27,-26,-25,36,37,38,39,

%U 40,41,30,31,32,33,34,35,24,25,26,27,28,29,18,19,20,21,22,23,12,13,14,15,16,17,6,7,8,9,10,11

%N Replace 6^k with (-6)^k in base 6 expansion of n.

%C Base 6 representation for n converted from base -6 to base 10.

%H Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, <a href="https://arxiv.org/abs/2012.04625">Finding structure in sequences of real numbers via graph theory: a problem list</a>, arXiv:2012.04625 [math.CO], 2020-2021.

%F a(6*k+m) = -6*a(k)+m for 0 <= m < 6. - _Chai Wah Wu_, Jan 16 2020

%t f[n_Integer, b_Integer] := Block[{l = IntegerDigits[n]}, Sum[l[[ -i]]*(-b)^(i - 1), {i, 1, Length[l]}]]; a = Table[ FromDigits[ IntegerDigits[n, 6]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 6]], {n, 1, 80}]; b

%Y Cf. A007092, A073787, A053985, A065369, A073791, A073792, A073794, A073795, A073796 & A073835.

%K base,easy,sign

%O 0,3

%A _Robert G. Wilson v_, Aug 12 2002