cp's OEIS Frontend

A317018 Sequence of distinct signed integers such that a(1) = 0 and for any n > 0, the negabinary representation of a(n+1) differ by exactly one digit from the negabinary representation of a(n) and has the smallest possible absolute value (in case of a tie, choose the integer with the rightmost difference).

%I A317018 #26 Feb 06 2024 19:31:33
%S A317018 0,1,-1,-2,2,3,5,-3,-4,4,20,12,8,6,7,9,-7,-8,-10,-6,-5,-9,-41,23,22,
%T A317018 24,25,29,27,26,28,36,-28,-12,-11,-13,-14,-18,14,15,17,-15,-16,16,80,
%U A317018 48,32,30,31,33,-31,-27,-29,-30,-34,-32,-40,-24,-20,-19,13,11,10
%N A317018 Sequence of distinct signed integers such that a(1) = 0 and for any n > 0, the negabinary representation of a(n+1) differ by exactly one digit from the negabinary representation of a(n) and has the smallest possible absolute value (in case of a tie, choose the integer with the rightmost difference).
%C A317018 This sequence has similarities with A316995; in both sequences, the absolute value of the difference of two consecutive terms is a power of 2.
%C A317018 This sequence also has similarities with A163252.
%H A317018 Rémy Sigrist, <a href="/A317018/b317018.txt">Table of n, a(n) for n = 1..10000</a>
%H A317018 Rémy Sigrist, <a href="/A317018/a317018.png">Line plot of the first 10000 terms</a>
%H A317018 Rémy Sigrist, <a href="/A317018/a317018.gp.txt">PARI program for A317018</a>
%H A317018 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a>.
%H A317018 Wikipedia, <a href="https://en.wikipedia.org/wiki/Negative_base">Negative base</a>.
%e A317018 The first terms, alongside their negabinary representation, are:
%e A317018   n   a(n)  nega(a(n))
%e A317018   --  ----  ----------
%e A317018    1     0        0
%e A317018    2     1        1
%e A317018    3    -1       11
%e A317018    4    -2       10
%e A317018    5     2      110
%e A317018    6     3      111
%e A317018    7     5      101
%e A317018    8    -3     1101
%e A317018    9    -4     1100
%e A317018   10     4      100
%e A317018   11    20    10100
%e A317018   12    12    11100
%e A317018   13     8    11000
%e A317018   14     6    11010
%e A317018   15     7    11011
%e A317018   16     9    11001
%e A317018   17    -7     1001
%e A317018   18    -8     1000
%e A317018   19   -10     1010
%e A317018   20    -6     1110
%o A317018 (PARI) See Links section.
%Y A317018 Cf. A039724, A163252, A212529, A316995.
%K A317018 sign,base
%O A317018 1,4
%A A317018 _Rémy Sigrist_, Jul 19 2018