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A062289
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Numbers n such that n-th row in Pascal triangle contains an even number, i.e., A048967(n) > 0.
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24
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2, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is 1 (Burns, 2016). - Amiram Eldar, Jan 26 2021
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LINKS
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Oliver Kullmann and Xishun Zhao, On variables with few occurrences in conjunctive normal forms, in: K. A. Sakallah and L. Simon (eds), International Conference on Theory and Applications of Satisfiability Testing, Springer, Berlin, Heidelberg, 2011, pp. 33-46; arXiv preprint, arXiv:1010.5756 [cs.DM], 2010-2011.
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FORMULA
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a(n) = 2 if n=1, otherwise max{min{2*i, a(n-i+1) + i}: 1 < i <= n}.
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MATHEMATICA
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PROG
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(Haskell)
a062289 n = a062289_list !! (n-1)
a062289_list = 2 : g 2 where
g n = nM n : g (n+1)
nM k = maximum $ map (\i -> i + min i (a062289 $ k-i+1)) [2..k]
-- Cf. link [Oliver Kullmann, Xishun Zhao], Def. 3.1, page 3.
(PARI) isok(m) = #select(x->((x%2)==0), vector(m+1, k, binomial(m, k-1))); \\ Michel Marcus, Jan 26 2021
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CROSSREFS
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Complement of A000225, so these might be called non-Mersenne numbers.
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001
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EXTENSIONS
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STATUS
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approved
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