A073794 Replace 7^k with (-7)^k in base 7 expansion of n.

0, 1, 2, 3, 4, 5, 6, -7, -6, -5, -4, -3, -2, -1, -14, -13, -12, -11, -10, -9, -8, -21, -20, -19, -18, -17, -16, -15, -28, -27, -26, -25, -24, -23, -22, -35, -34, -33, -32, -31, -30, -29, -42, -41, -40, -39, -38, -37, -36, 49, 50, 51, 52, 53, 54, 55, 42, 43, 44, 45, 46, 47, 48, 35, 36, 37, 38, 39, 40, 41

Offset: 0

Author

Robert G. Wilson v, Aug 12 2002

Keywords

• base
• easy
• sign

Comments

Base 7 representation for n (in lexicographic order) converted from base -7 to base 10.

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. A007093, A073788, A053985, A065369, A073791, A073792, A073793, A073795, A073796 & A073835.

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, 7]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 7]], {n, 1, 80}]; b

Formula

a(7*k+m) = -7*a(k)+m for 0 <= m < 7. - Chai Wah Wu, Jan 16 2020