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A356964 Replace 2^k in binary expansion of n with tribonacci(k+3) (where tribonacci corresponds to A000073).

%I A356964 #16 Sep 11 2022 06:13:26
%S A356964 0,1,2,3,4,5,6,7,7,8,9,10,11,12,13,14,13,14,15,16,17,18,19,20,20,21,
%T A356964 22,23,24,25,26,27,24,25,26,27,28,29,30,31,31,32,33,34,35,36,37,38,37,
%U A356964 38,39,40,41,42,43,44,44,45,46,47,48,49,50,51,44,45,46,47
%N A356964 Replace 2^k in binary expansion of n with tribonacci(k+3) (where tribonacci corresponds to A000073).
%C A356964 This sequence is to tribonacci numbers (A000073) what A022290 is to Fibonacci numbers (A000045).
%C A356964 For any k >= 0, k appears A117546(k) times in this sequence.
%H A356964 Rémy Sigrist, <a href="/A356964/b356964.txt">Table of n, a(n) for n = 0..8192</a>
%H A356964 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A356964 a(A003726(n+1)) = n.
%F A356964 a(A003796(n+1)) = n.
%e A356964 For n = 9:
%e A356964 - 9 = 2^3 + 2^0,
%e A356964 - so a(9) = A000073(3+3) + A000073(0+3) = 7 + 1 = 8.
%o A356964 (PARI) a(n) = { my (v=0, k); while (n, n-=2^k=valuation(n,2); v+=([0,1,0; 0,0,1; 1,1,1]^(3+k))[2,1]); return (v); }
%o A356964 (Python)
%o A356964 def A356964(n):
%o A356964     a, b, c, s = 1,2,4,0
%o A356964     for i in bin(n)[-1:1:-1]:
%o A356964         s += int(i)*a
%o A356964         a, b, c = b, c, a+b+c
%o A356964     return s # _Chai Wah Wu_, Sep 10 2022
%Y A356964 Cf. A000073, A003726, A003796, A022290, A117546.
%K A356964 nonn,base
%O A356964 0,3
%A A356964 _Rémy Sigrist_, Sep 06 2022