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A353624 a(0) = 0, and for n > 0, a(n) is the least multiple of n that can be added to n without carries in balanced ternary.

%I A353624 #10 May 01 2022 11:42:33
%S A353624 0,2,6,6,8,30,18,21,16,18,20,55,24,26,84,90,80,51,54,57,60,63,132,46,
%T A353624 48,75,52,54,56,87,60,62,288,165,408,70,72,74,456,78,80,246,252,516,
%U A353624 484,270,276,658,240,441,400,153,156,159,162,165,168,171,522,649
%N A353624 a(0) = 0, and for n > 0, a(n) is the least multiple of n that can be added to n without carries in balanced ternary.
%C A353624 Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
%H A353624 Rémy Sigrist, <a href="/A353624/b353624.txt">Table of n, a(n) for n = 0..10000</a>
%H A353624 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%F A353624 a(n) = n * A353623(n).
%F A353624 a(3*n) = 3*a(n).
%e A353624 For n = 5:
%e A353624 - we consider the following cases:
%e A353624       k  bter(k*5)  carries?
%e A353624       -  ---------  --------
%e A353624       1        1TT  yes
%e A353624       2        101  yes
%e A353624       3       1TT0  yes
%e A353624       4       1T1T  yes
%e A353624       5       10T1  yes
%e A353624       6       1010  no
%e A353624 - so a(5) = 6*5 = 30.
%o A353624 (PARI) ok(u,v) = { while (u && v, my (uu=[0,+1,-1][1+u%3], vv=[0,+1,-1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) }
%o A353624 a(n) = for (k=1, oo, if (ok(n, n*k), return (n*k)))
%Y A353624 Cf. A059095, A261892 (binary analog), A353623.
%K A353624 nonn,base
%O A353624 0,2
%A A353624 _Rémy Sigrist_, Apr 30 2022