A316823 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.

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

Offset: 0

Author

Jackson Haselhorst, Aug 26 2019

Keywords

• sign
• base

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..6560

Crossrefs

Cf. A007095, A117966, A309991, A309995.

Column k=4 of A319047.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      9*a(iquo(n, 9))+mods(n, 9))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 26 2019

PARI

f(x) = if (x > 9/2, -(9-x), x);
a(n) = subst(Pol(apply(x->f(x), digits(n, 9)), 'x), 'x, 9); \\ Michel Marcus, Aug 27 2019