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The binary expansions of A352909(n+1, 1) and A352909(n+1, 2) encode respectively the 1's and the 2's in the ternary expansion of a(n).
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%I #13 May 03 2022 17:05:25

%S 0,2,1,6,3,8,7,5,4,18,9,20,19,11,10,24,21,15,12,26,25,23,22,17,16,14,

%T 13,54,27,56,55,29,28,60,57,33,30,62,61,59,58,35,34,32,31,72,63,45,36,

%U 74,73,65,64,47,46,38,37,78,75,69,66,51,48,42,39,80,79,77

%N The binary expansions of A352909(n+1, 1) and A352909(n+1, 2) encode respectively the 1's and the 2's in the ternary expansion of a(n).

%C This sequence is a permutation of the nonnegative integers with inverse A353661.

%H Rémy Sigrist, <a href="/A353660/b353660.txt">Table of n, a(n) for n = 0..6560</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A005836(A352909(n+1, 1)) + 2*A005836(A352909(n+1, 2)).

%F a(n) < 3^k iff n < 3^k.

%e For n = 42:

%e - A352909(43, 1) = 9,

%e - A352909(43, 2) = 2,

%e - the binary expansion of 9 is "1001",

%e - the binary expansion of 2 is "10",

%e - so the ternary expansion of a(42) is "1021",

%e - and a(42) = 34.

%o (PARI) b2t(n) = fromdigits(binary(n), 3)

%o { n=-1; for (d=0, 2^8-1, for (k=0, d, if (bitand(t1=k, t2=d-k)==0, print1 (b2t(t1) + 2*b2t(t2)", "); if (n++==67, break (2))))) }

%Y Cf. A005836, A352909, A353661 (inverse), A353662.

%K nonn,look,base

%O 0,2

%A _Rémy Sigrist_, May 02 2022