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%I #19 May 03 2019 21:36:09
%S 1,2,3,4,6,8,9,10,12,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,36,
%T 40,42,44,45,46,48,50,51,52,54,56,57,58,60,63,64,66,68,69,70,72,75,76,
%U 78,80,81,82,84,85,86,87,88,90,92,93,94,96,100
%N Smallest number greater than a(n-1) divisible by smallest number that is not a divisor of a(n-1).
%C Conjecture: Numbers that are not in this sequence below any finite limit will never outnumber numbers that are.
%C That is, a(n) < 2n for all n. This holds for n < 10^10. - _Charles R Greathouse IV_, Apr 14 2014
%C The expected value of the first differences of this sequence is Sum_{q>=2} (q(p-1)/(2*lcm(2,...,q)) as q = p^k ranges over the prime powers, or approximately 1.39389022808623327303..., so the conjecture is very likely to be true. - _Charlie Neder_, Apr 26 2019
%H Charles R Greathouse IV, <a href="/A240911/b240911.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) cannot be 5 because smallest number that is not a divisor of 4 is 3 and 3 is not a divisor of 5.
%o (PARI) step(n)=for(k=2,n+1,if(n%k,return((n\k+1)*k)))
%o v=vector(100);v[1]=1;for(n=2,#v,v[n]=step(v[n-1])); v \\ _Charles R Greathouse IV_, Apr 14 2014
%K nonn,easy
%O 1,2
%A _J. Lowell_, Apr 14 2014
%E a(26)-a(63) from _Charles R Greathouse IV_, Apr 14 2014
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