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A305238 Negative numbers in base -10.

%I A305238 #14 Feb 16 2025 08:33:54
%S A305238 19,18,17,16,15,14,13,12,11,10,29,28,27,26,25,24,23,22,21,20,39,38,37,
%T A305238 36,35,34,33,32,31,30,49,48,47,46,45,44,43,42,41,40,59,58,57,56,55,54,
%U A305238 53,52,51,50,69,68,67,66,65,64,63,62,61,60,79,78,77,76,75
%N A305238 Negative numbers in base -10.
%C A305238 a(n) = A039723(-n).
%C A305238 Also base -10 representation of -n reinterpreted as decimal numbers.
%C A305238 The first comment is slightly misleading because sequence A039723 isn't defined for n < 0, and none of the terms a(n) here is a term of A039723. However, it can be seen as the definition of the extension of A039723 to negative indices. Also, the (naïve) recursive definition or implementation of A039723 requires that function to be defined for negative arguments, and using the generic formula it will work as expected for -n, n > 0. - _M. F. Hasler_, Oct 16 2018
%H A305238 Jianing Song, <a href="/A305238/b305238.txt">Table of n, a(n) for n = 1..10000</a>
%H A305238 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negadecimal.html">Negadecimal</a>
%H A305238 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a>
%H A305238 Wikipedia, <a href="http://en.wikipedia.org/wiki/Negative_base">Negative base</a>
%e A305238 -1 in base -10 is represented as 19 (1*(-10) + 9 = -1), so a(1) = 19;
%e A305238 -11 in base -10 is represented as 29 (2*(-10) + 9 = -11), so a(11) = 29;
%e A305238 -99 in base -10 is represented as 1901 (1*(-10)^3 + 9*(-10)^2 + 1 = -99), so a(99) = 1901.
%o A305238 (PARI) A305238(n)=A039723(-n) \\ _M. F. Hasler_, Oct 16 2018
%Y A305238 Cf. A039724 (nonnegative numbers in base -2), A212529 (negative numbers in base -2), A007608 (nonnegative numbers in base -4), A212526 (negative numbers in base -4), A039723 (nonnegative numbers in base -10).
%K A305238 nonn,base,easy
%O A305238 1,1
%A A305238 _Jianing Song_, Jun 19 2018