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%I #17 Dec 09 2020 01:55:01
%S 0,1,2,3,4,5,6,7,8,9,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,-20,-19,-18,-17,
%T -16,-15,-14,-13,-12,-11,-30,-29,-28,-27,-26,-25,-24,-23,-22,-21,-40,
%U -39,-38,-37,-36,-35,-34,-33,-32,-31,-50,-49,-48,-47,-46,-45,-44,-43,-42,-41,-60
%N Replace 10^k with (-10)^k in decimal expansion of n.
%C Base 10 representation for n (in lexicographic order) converted from base -10 to base 10.
%C A bijection from N = [0..oo) to Z = (-oo..+oo), or enumeration of the integers. - _M. F. Hasler_, Oct 17 2018
%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, Dec 08, 2020
%F a(10*k+m) = -10*a(k)+m for 0 <= m < 10. - _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, 10]], {n, 0, 80}]; b = {}; Do[ b = Append[b, f[a[[n]], 10]], {n, 1, 80}]; b (* Typo fixed by _Harvey P. Dale_, Oct 03 2013 *)
%o (PARI) a(n)=fromdigits(digits(n),-10) \\ _M. F. Hasler_, Oct 17 2018
%Y Cf. A001477, A039723, A053985, A065369, A073791, A073792, A073793, A073794, A073795 & A073796.
%K base,easy,sign
%O 0,3
%A _Robert G. Wilson v_, Aug 12 2002
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