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A309995 Balanced septenary enumeration (or balanced septenary representation) of integers; write n in septenary and then replace 4's with (-3),s, 5's with (-2)'s, and 6's with (-1)'s.

%I A309995 #23 Aug 29 2019 20:22:39
%S A309995 0,1,2,3,-3,-2,-1,7,8,9,10,4,5,6,14,15,16,17,11,12,13,21,22,23,24,18,
%T A309995 19,20,-21,-20,-19,-18,-24,-23,-22,-14,-13,-12,-11,-17,-16,-15,-7,-6,
%U A309995 -5,-4,-10,-9,-8,49,50,51,52,46,47,48,56,57,58,59,53,54,55,63
%N A309995 Balanced septenary enumeration (or balanced septenary representation) of integers; write n in septenary and then replace 4's with (-3),s, 5's with (-2)'s, and 6's with (-1)'s.
%C A309995 This sequence, like the balanced ternary and quinary sequences, includes every integer exactly once.
%H A309995 Alois P. Heinz, <a href="/A309995/b309995.txt">Table of n, a(n) for n = 0..16806</a>
%e A309995 As 54_10 = 105_7, the digits of 54 in base 7 are 1, 0 and 5. 5 > 3 so it's replaced by -2. The digits then are 1, 0 and -2 giving a(54) = 1*7^2 + 0 * 7^1 + (-2) * 7^0 = 49 + 0 - 2 = 47. - _David A. Corneth_, Aug 26 2019
%p A309995 a:= proc(n) option remember; `if`(n=0, 0,
%p A309995       7*a(iquo(n, 7))+mods(n, 7))
%p A309995     end:
%p A309995 seq(a(n), n=0..100);  # _Alois P. Heinz_, Aug 26 2019
%o A309995 (PARI) a(n,b=7) = fromdigits(apply(d -> if (d<b/2, d, d-b), digits(n, b)), b) \\ _Rémy Sigrist_, Aug 26 2019
%o A309995 (PARI) a(n) = my(d = digits(n, 7)); for(i = 1, #d, if(d[i] > 3, d[i]-=7)); fromdigits(d, 7) \\ _David A. Corneth_, Aug 26 2019
%Y A309995 Cf. A007093, A117966, A309991.
%Y A309995 Column k=3 of A319047.
%K A309995 base,sign
%O A309995 0,3
%A A309995 _Jackson Haselhorst_, Aug 26 2019