A065369 Replace 3^k with (-3)^k in ternary expansion of n.

0, 1, 2, -3, -2, -1, -6, -5, -4, 9, 10, 11, 6, 7, 8, 3, 4, 5, 18, 19, 20, 15, 16, 17, 12, 13, 14, -27, -26, -25, -30, -29, -28, -33, -32, -31, -18, -17, -16, -21, -20, -19, -24, -23, -22, -9, -8, -7, -12, -11, -10, -15, -14, -13, -54, -53, -52, -57, -56, -55, -60, -59, -58, -45, -44, -43, -48, -47, -46

Offset: 0

Author

Marc LeBrun, Oct 31 2001

Keywords

• base
• easy
• look
• sign

Comments

Base 3 representation for n (in lexicographic order) converted from base -3 to base 10.

Notation: (3)[n](-3)

Fixed point of the morphism 0-> 0,1,2 ; 1-> -3,-2,-1 ; 2-> -6,-5,-4 ; ...; n-> -3n,-3n+1,-3n+2. - Philippe Deléham, Oct 22 2011

Examples

			15 = +1(9)+2(3)+0(1) -> +1(+9)+2(-3)+0(+1) = +3 = a(15)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..19682
• 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 [math.CO], 2020-2021.

Crossrefs

Cf. A007089, A053985, A065367, A073785, A073791, A073792, A073793, A073794, 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, 3]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 3]], {n, 1, 80}]; b

PARI

a(n) = fromdigits(digits(n, 3), -3) \\ Rémy Sigrist, Feb 06 2020

Formula

a(n) = Sum_{k>=0} A030341(n,k)*(-3)^k. - Philippe Deléham, Oct 22 2011

a(3*k+m) = -3*a(k)+m for 0 <= m < 3. - Chai Wah Wu, Jan 16 2020