A073791 Replace 4^k with (-4)^k in base 4 expansion of n.

0, 1, 2, 3, -4, -3, -2, -1, -8, -7, -6, -5, -12, -11, -10, -9, 16, 17, 18, 19, 12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 32, 33, 34, 35, 28, 29, 30, 31, 24, 25, 26, 27, 20, 21, 22, 23, 48, 49, 50, 51, 44, 45, 46, 47, 40, 41, 42, 43, 36, 37, 38, 39, -64, -63, -62, -61, -68, -67, -66, -65, -72, -71, -70, -69

Offset

0,3

Comments

Base 4 representation for n converted from base -4 to base 10.

Links

Table of n, a(n) for n=0..75.

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.

Formula

a(4*k+m) = -4*a(k)+m for 0 <= m < 4. - Chai Wah Wu, Jan 16 2020

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, 4]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 4]], {n, 1, 80}]; b

Prog

(PARI) a(n) = subst(Pol(digits(n, 4)), x, -4); \\ Michel Marcus, Jan 30 2019

Crossrefs

Cf. A007090, A007608, A053985, A065369, A073792, A073793, A073794, A073795, A073796 & A073835.

Cf. A066321, A320283.

Sequence in context: A028356 A232244 A260644 * A350862 A030340 A122453

Adjacent sequences: A073788 A073789 A073790 * A073792 A073793 A073794

Keyword

base,easy,sign

Author

Robert G. Wilson v, Aug 12 2002

Status

approved