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Smallest k such that either k >= n and k is a power of 2, or k >= 5n/3 and the prime divisors of k are precisely 2 and 5.
1

%I #12 Dec 19 2017 14:11:30

%S 1,2,4,4,8,8,8,8,16,16,16,16,16,16,16,16,32,32,32,32,32,32,32,32,32,

%T 32,32,32,32,32,32,32,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,

%U 64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,128,128

%N Smallest k such that either k >= n and k is a power of 2, or k >= 5n/3 and the prime divisors of k are precisely 2 and 5.

%C First disagreement with A062383(n-1) is at n = 129.

%C For n > 2, a(n) is not squarefree. - _Iain Fox_, Dec 17 2017

%H Eric M. Schmidt, <a href="/A296613/b296613.txt">Table of n, a(n) for n = 1..10000</a>

%H Bernadette Faye, Florian Luca, Pieter Moree, <a href="https://arxiv.org/abs/1708.03563">On the discriminator of Lucas sequences</a>, arXiv:1708.03563 [math.NT], 2017, Theorem 1.

%o (PARI) a(n) = for(k=n, +oo, if(k == 2^valuation(k, 2) || (k >= 5*n/3 && factor(k)[, 1] == [2, 5]~), return(k))) \\ _Iain Fox_, Dec 17 2017

%Y Cf. A033846.

%K nonn

%O 1,2

%A _Eric M. Schmidt_, Dec 16 2017