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Balanced nonary enumeration (or balanced nonary representation) of integers; write n in nonary (base 9) and then replace 5's with (-4)'s, 6's with (-3)'s, 7's with (-2)'s, and 8's with (-1)'s.
2

%I #26 Aug 29 2019 20:26:55

%S 0,1,2,3,4,-4,-3,-2,-1,9,10,11,12,13,5,6,7,8,18,19,20,21,22,14,15,16,

%T 17,27,28,29,30,31,23,24,25,26,36,37,38,39,40,32,33,34,35,-36,-35,-34,

%U -33,-32,-40,-39,-38,-37,-27,-26,-25,-24,-23,-31,-30,-29,-28

%N Balanced nonary enumeration (or balanced nonary representation) of integers; write n in nonary (base 9) and then replace 5's with (-4)'s, 6's with (-3)'s, 7's with (-2)'s, and 8's with (-1)'s.

%H Alois P. Heinz, <a href="/A316823/b316823.txt">Table of n, a(n) for n = 0..6560</a>

%e Since 35_10=38_9, the digits of 35 in base 9 are 3 and 8. 8>4, so it is replaced with (-1). The digits are then 3 and -1, so a(35)=3*9^1+(-1)*9^0=27-1=26.

%p a:= proc(n) option remember; `if`(n=0, 0,

%p 9*a(iquo(n, 9))+mods(n, 9))

%p end:

%p seq(a(n), n=0..100); # _Alois P. Heinz_, Aug 26 2019

%o (PARI) f(x) = if (x > 9/2, -(9-x), x);

%o a(n) = subst(Pol(apply(x->f(x), digits(n, 9)), 'x), 'x, 9); \\ _Michel Marcus_, Aug 27 2019

%Y Cf. A007095, A117966, A309991, A309995.

%Y Column k=4 of A319047.

%K sign,base

%O 0,3

%A _Jackson Haselhorst_, Aug 26 2019