A320636 Negative numbers in base -3.

12, 11, 10, 22, 21, 20, 1202, 1201, 1200, 1212, 1211, 1210, 1222, 1221, 1220, 1102, 1101, 1100, 1112, 1111, 1110, 1122, 1121, 1120, 1002, 1001, 1000, 1012, 1011, 1010, 1022, 1021, 1020, 2202, 2201, 2200, 2212, 2211, 2210, 2222, 2221, 2220, 2102, 2101, 2100, 2112

Offset

1,1

Comments

Extend A073785 to negative-indexed terms, then a(n) = A073785(-n).

Links

Table of n, a(n) for n=1..46.

Eric Weisstein's World of Mathematics, Negadecimal

Eric Weisstein's World of Mathematics, Negabinary

Wikipedia, Negative base

Example

-7 in base -3 is represented as 1202 (1*(-3)^3 + 2*(-3)^2 + 2 = -7), so a(7) = 1202;
-16 in base -3 is represented as 1102 (1*(-3)^3 + 1*(-3)^2 + 2 = -16), so a(16) = 1102;
-40 in base -3 is represented as 2222 (2*(-3)^3 + 2*(-3)^2 + 2*(-3) + 2 = -99), so a(40) = 2222.

Prog

(PARI) A073785 = base(n, b=-3) = if(n, base(n\b, b)*10 + n%b, 0)
a(n) = A073785(-n)
(Python)
def A073785(n): # after Reinhard Zumkeller
    if n == 0: return 0
    (q, r) = divmod(n, -3)
    (nn, m) = (q, r) if r >= 0 else (q+1, r+3)
    return A073785(nn)*10 + m
def a(n): return A073785(-n)
print([a(n) for n in range(1, 47)]) # Michael S. Branicky, Dec 11 2021

Crossrefs

Nonnegative numbers in negative bases: A039723 (b=-10), A039724 (b=-2), A073785 (b=-3), A007608 (b=-4), A073786 (b=-5), A073787 (b=-6), A073788 (b=-7), A073789 (b=-8), A073790 (b=-9).

Negative numbers in negative bases: A305238 (b=-10), A212529 (b=-2), this sequence (b=-3), A212526 (b=-4).

Sequence in context: A022968 A023454 A055123 * A070560 A358497 A019330

Adjacent sequences: A320633 A320634 A320635 * A320637 A320638 A320639

Keyword

nonn,base

Author

Jianing Song, Oct 18 2018

Status

approved