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A265418 a(1)=2; for n>1, a(n) is the least prime q greater than p = a(n-1) such that p/q reaches a new minimum.

%I A265418 #11 Jan 12 2016 00:49:56
%S A265418 2,3,5,11,29,79,223,631,1787,5077,14431,41023,116639,331651,943031,
%T A265418 2681467,7624649,21680413,61647497,175292519,498438203,1417291781,
%U A265418 4030020143,11459222851,32583903763,92651203181,263450491193,749112358279,2130075077051,6056794796849,17222286484817
%N A265418 a(1)=2; for n>1, a(n) is the least prime q greater than p = a(n-1) such that p/q reaches a new minimum.
%C A265418 Inspired by the fact that 294911/235927 = 1.2500095368..., two primes together with 2^16 form a primitive weird number (A002975(9729)).
%C A265418 p/q ->
%C A265418 0.3516835469078526298668938767771073728
%C A265418 ...
%C A265418 Each pair of initial primes, p & q, will yield a different ratio.
%H A265418 Robert G. Wilson v, <a href="/A265418/b265418.txt">Table of n, a(n) for n = 1..1620</a>
%e A265418 2/3 is 0.666... is a new low or minimum;
%e A265418 3/5 is 0.600... is a new minimum;
%e A265418 5/11 is 0.454... is a new minimum;
%e A265418 11/29 is 0.379... is a new minimum;
%e A265418 29/79 is 0.367... is a new minimum;
%e A265418 ... 6056794796849/17222286484817 is 0.351... is a new minimum; etc.
%t A265418 f[lst_List] := Block[{p = lst[[-2]], q = lst[[-1]]}, Append[lst, NextPrime[q^2/p]]]; Nest[f, {2, 3}, 29]
%K A265418 nonn
%O A265418 1,1
%A A265418 _Robert G. Wilson v_, Dec 08 2015