A073835 Replace 10^k with (-10)^k in decimal expansion of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -60

Offset: 0

Author

Robert G. Wilson v, Aug 12 2002

Keywords

• base
• easy
• sign

Comments

Base 10 representation for n (in lexicographic order) converted from base -10 to base 10.

A bijection from N = [0..oo) to Z = (-oo..+oo), or enumeration of the integers. - M. F. Hasler, Oct 17 2018

Links

• Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625, Dec 08, 2020

Crossrefs

Cf. A001477, A039723, A053985, A065369, A073791, A073792, A073793, A073794, A073795 & A073796.

Programs

Mathematica

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 *)

PARI

a(n)=fromdigits(digits(n),-10) \\ M. F. Hasler, Oct 17 2018

Formula

a(10*k+m) = -10*a(k)+m for 0 <= m < 10. - Chai Wah Wu, Jan 16 2020