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 A080702 a(1)=3; for n>1, a(n) = smallest number > a(n-1) such that the condition "if n is in the sequence then a(n) is even" is satisfied. 0

%I

%S 3,4,6,8,9,10,11,12,14,16,18,20,21,22,23,24,25,26,27,28,30,32,34,36,

%T 38,40,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,64,66,

%U 68,70,72,74,76,78,80,82,84,86,88,90,92,93,94,95,96,97,98,99,100,101,102

%N a(1)=3; for n>1, a(n) = smallest number > a(n-1) such that the condition "if n is in the sequence then a(n) is even" is satisfied.

%D Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

%F {a(a(n))} = {2i : i >= 3}.

%o (PARI) lista(nn) = {v = vector(nn); v[1] = 3; prev = v[1]; for (n=2, nn, new = prev+1; if (vecsearch(vecsort(v,,8), n) && (new % 2), new ++); v[n] = new; prev = new;); v;} \\ _Michel Marcus_, Feb 16 2015

%Y Equals A079945(n+1) - 1.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Mar 01 2003

%E More terms from _Matthew Vandermast_, Mar 05 2003

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Last modified June 24 07:31 EDT 2021. Contains 345416 sequences. (Running on oeis4.)