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A237288 Lexicographically earliest sequence of noncomposite numbers such that a(n)*n / sum(i=1..n, a(n) ) is strictly increasing. 1

%I

%S 1,2,3,5,7,11,17,23,31,41,53,67,83,101,127,151,179,211,251,293,337,

%T 389,443,503,569,641,719,809,907,1009,1117,1229,1361,1493,1637,1787,

%U 1949,2129,2309,2503,2707,2917,3137,3371,3613,3877,4153,4441,4751,5059,5381

%N Lexicographically earliest sequence of noncomposite numbers such that a(n)*n / sum(i=1..n, a(n) ) is strictly increasing.

%C If we replace in name of sequence:

%C noncomposite numbers -> nonprime numbers, then a(n) = A103517(n-1),

%C noncomposite numbers -> composite numbers, then a(n) = A103517(n),

%C noncomposite numbers -> primes, then a(n) = A237285(n),

%C noncomposite numbers -> natural numbers, then a(n) = A000027(n).

%e For n=8: noncomposite number a(8) = 23 > a(7) = 17 is the smallest noncomposite number such that (8*23 / 69) > (7*17 / 46), a(8) is not 19 because (8*19 / (69-4)) < (7*17 / 46).

%Y Cf. A008578 (noncomposite numbers).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Feb 28 2014

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Last modified May 27 11:09 EDT 2022. Contains 354096 sequences. (Running on oeis4.)