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A309991 Balanced quinary (base 5) enumeration (or balanced quinary representation) of integers, write n in quinary, and then replace 3's with (-2)'s and 4's with (-1)'s.

%I A309991 #23 Sep 05 2020 11:40:16
%S A309991 0,1,2,-2,-1,5,6,7,3,4,10,11,12,8,9,-10,-9,-8,-12,-11,-5,-4,-3,-7,-6,
%T A309991 25,26,27,23,24,30,31,32,28,29,35,36,37,33,34,15,16,17,13,14,20,21,22,
%U A309991 18,19,50,51,52,48,49,55,56,57,53,54,60,61,62,58,59,40,41
%N A309991 Balanced quinary (base 5) enumeration (or balanced quinary representation) of integers, write n in quinary, and then replace 3's with (-2)'s and 4's with (-1)'s.
%C A309991 This sequence, like the balanced ternary sequence, will eventually include every integer exactly once.
%H A309991 Alois P. Heinz, <a href="/A309991/b309991.txt">Table of n, a(n) for n = 0..15624</a>
%p A309991 a:= proc(n) option remember; `if`(n=0, 0,
%p A309991       5*a(iquo(n, 5))+mods(n, 5))
%p A309991     end:
%p A309991 seq(a(n), n=0..100);  # _Alois P. Heinz_, Aug 26 2019
%t A309991 Table[FromDigits[IntegerDigits[n,5]/.{3->-2,4->-1},5],{n,0,120}] (* _Harvey P. Dale_, Sep 05 2020 *)
%o A309991 (PARI) a(n) = subst(Pol(apply(d->if(d>2, d-5, d), digits(n, 5)), 'x), 'x, 5) \\ _Andrew Howroyd_, Aug 26 2019
%Y A309991 Cf. A117966.
%Y A309991 Column k=2 of A319047.
%K A309991 sign,base
%O A309991 0,3
%A A309991 _Jackson Haselhorst_, Aug 26 2019