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%I #5 Mar 18 2024 09:51:23
%S 0,1,2,2,1,2,3,3,3,2,3,2,2,1,2,3,3,4,3,4,4,4,3,3,4,4,3,2,3,4,4,3,2,3,
%T 3,3,2,3,2,2,1,2,3,3,4,3,4,4,4,3,4,5,5,4,3,4,5,5,4,4,5,5,5,4,5,4,4,3,
%U 3,4,4,5,4,5,5,5,4,3,4,4,3,2,3,4,4,3,4
%N a(n) is the number of runs in the balanced ternary expansion of n.
%C Leading zeros are ignored.
%C Every positive integers occurs infinitely many times.
%F a(n) <= A134021(n).
%F a(A153773(k)) = k for any k > 0.
%e The first terms, alongside the balanced ternary expansion of n, are:
%e n a(n) bter(n)
%e --- ---- -------
%e 0 0 0
%e 1 1 1
%e 2 2 1T
%e 3 2 10
%e 4 1 11
%e 5 2 1TT
%e 6 3 1T0
%e 7 3 1T1
%e 8 3 10T
%e 9 2 100
%e 10 3 101
%e 11 2 11T
%e 12 2 110
%e 13 1 111
%e 14 2 1TTT
%e 15 3 1TT0
%o (PARI) a(n) = { my (r = 0, d); while (n, r++; d = centerlift(Mod(n, 3)); while (d==centerlift(Mod(n, 3)), n = (n-d)/3;);); return (r); }
%Y Cf. A005811, A043555, A134021, A153773, A297770.
%K nonn,base,easy
%O 0,3
%A _Rémy Sigrist_, Mar 17 2024