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A353158 a(n) is the distance from n to the nearest integer that can be added to n without carries in base 3.

%I A353158 #12 May 01 2022 11:42:44
%S A353158 0,0,1,0,0,2,3,2,1,0,0,1,0,0,2,4,6,8,9,8,7,6,5,4,3,2,1,0,0,1,0,0,2,3,
%T A353158 2,1,0,0,1,0,0,2,4,6,8,10,12,14,16,18,20,22,24,26,27,26,25,24,23,22,
%U A353158 21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4
%N A353158 a(n) is the distance from n to the nearest integer that can be added to n without carries in base 3.
%H A353158 Rémy Sigrist, <a href="/A353158/b353158.txt">Table of n, a(n) for n = 0..9841</a>
%F A353158 a(n) = 0 iff n belongs to A005836.
%e A353158 For n = 42:
%e A353158 - the numbers k around 42, alongside their distance to 42, ternary expansion and whether they require carries when added to 42, are:
%e A353158       k   d  ter(k)  carries?
%e A353158       --  -  ------  --------
%e A353158       38  4    1102  no
%e A353158       39  3    1110  yes
%e A353158       40  2    1111  yes
%e A353158       41  1    1112  yes
%e A353158       42  0    1120  yes
%e A353158       43  1    1121  yes
%e A353158       44  2    1122  yes
%e A353158       45  3    1200  yes
%e A353158       46  4    1201  yes
%e A353158 - so a(42) = 4.
%o A353158 (PARI) ok(u,v) = sumdigits(u+v,3)==sumdigits(u,3)+sumdigits(v,3)
%o A353158 a(n) = { for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d))) }
%Y A353158 Cf. A005836 (positions of zeros), A167877, A353157 (binary variant).
%K A353158 nonn,base
%O A353158 0,6
%A A353158 _Rémy Sigrist_, Apr 27 2022