login
Replace 5^k with (-5)^k in base 5 expansion of n.
8

%I #14 Jan 15 2024 11:03:38

%S 0,1,2,3,4,-5,-4,-3,-2,-1,-10,-9,-8,-7,-6,-15,-14,-13,-12,-11,-20,-19,

%T -18,-17,-16,25,26,27,28,29,20,21,22,23,24,15,16,17,18,19,10,11,12,13,

%U 14,5,6,7,8,9,50,51,52,53,54,45,46,47,48,49,40,41,42,43,44,35,36,37,38,39,30,31,32,33,34

%N Replace 5^k with (-5)^k in base 5 expansion of n.

%C Base 5 representation for n converted from base -5 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(5*k+m) = -5*a(k)+m for 0 <= m < 5. - _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, 5]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 5]], {n, 1, 80}]; b

%Y Cf. A007091, A073786, A053985, A065369, A073791, A073793, A073794, A073795, A073796 & A073835.

%K base,easy,sign

%O 0,3

%A _Robert G. Wilson v_, Aug 12 2002