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A089080 Sequence is S(infinity) where S(1)={1,2} and S(n)=S(n-1)S'(n-1), where S'(k) is obtained from S(k) by replacing the single 1 with the least integer not occurring in S(k).

%I A089080 #17 Nov 26 2024 12:02:29
%S A089080 1,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7,2,
%T A089080 3,2,4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,8,2,3,2,
%U A089080 4,2,3,2,5,2,3,2,4,2,3,2,6,2,3,2,4,2,3,2,5,2,3,2,4,2,3,2,7,2,3,2,4,2,3,2,5
%N A089080 Sequence is S(infinity) where S(1)={1,2} and S(n)=S(n-1)S'(n-1), where S'(k) is obtained from S(k) by replacing the single 1 with the least integer not occurring in S(k).
%H A089080 Antti Karttunen, <a href="/A089080/b089080.txt">Table of n, a(n) for n = 1..16384</a>
%F A089080 Sum_{k=1..n} a(k) = 3*n+O(log(n)) ( Sum_{k=1..n} a(k) < 3*n )
%e A089080 S(1)={1,2} then S'(1)={3,2} and sequence begins 1,2,3,2
%o A089080 (PARI)
%o A089080 A085058(n) = (valuation(n+1, 2)+2);
%o A089080 A089080(n) = if(1==n,n,A085058(n-2)); \\ _Antti Karttunen_, Nov 01 2018
%Y A089080 Essentially the same as A085058 (with prepended 1 and different indexing).
%Y A089080 Cf. A094267 (first differences), A208147 (partial products).
%K A089080 nonn,easy
%O A089080 1,2
%A A089080 _Benoit Cloitre_, Dec 04 2003