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%I #110 May 01 2022 11:42:30
%S 0,1,1,2,1,1,2,4,4,5,4,4,2,1,1,2,4,4,5,7,10,11,13,10,11,13,13,14,13,
%T 13,11,10,13,11,10,7,5,4,4,2,1,1,2,4,4,5,7,10,11,13,10,11,13,13,14,16,
%U 19,20,22,28,29,31,31,32,34,37,38,40,28,29,31,31,32
%N a(n) is the distance from n to the nearest integer that can be added to n without carries in balanced ternary.
%C Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
%H Rémy Sigrist, <a href="/A352501/b352501.txt">Table of n, a(n) for n = 0..9841</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%F a(n) = 1 iff n > 0 and n belongs to A003462 or A007051.
%F a(3*n) = 3*a(n)+1 for any n > 0.
%e For n = 7:
%e - the numbers k around 7, alongside their distance to 7, balanced ternary expansion and whether they require carries when added to 7, are:
%e k d bter(k) carries?
%e -- - ------- --------
%e 3 4 10 no
%e 4 3 11 yes
%e 5 2 1TT yes
%e 6 1 1T0 yes
%e 7 0 1T1 yes
%e 8 1 10T yes
%e 9 2 100 yes
%e 10 3 101 yes
%e 11 4 11T yes
%e - so a(7) = 4.
%o (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 a(n) = for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d)))
%Y Cf. A003462, A007051, A059095, A353158.
%K nonn,base
%O 0,4
%A _Rémy Sigrist_, Apr 28 2022
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