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%I #7 Dec 09 2021 17:25:15
%S 2,4,6,8,9,11,14,15,18,21,23,24,27,29,30,32,34,36,39,42,44,46,50,51,
%T 53,58,61,62,65,66,68,70,71,72,76,77,79,80,82,84,86,87,90,91,94,96,97,
%U 99,101,105,106,110,114,117,118,121,123,124,125,127,132,135
%N Numbers k such that prime(k)^2 < prime(k-1)*prime(k+1).
%C If 1 is appended to A046868, the resulting sequence is the complement of A233671. Does A233671 have asymptotic density 1/2? Does every positive integer occur infinitely many times in the difference sequence of A233671?
%H Clark Kimberling, <a href="/A233671/b233671.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 2 because 3^2 < 2*5.
%t Select[Range[2, 200], Prime[#]^2 < Prime[# - 1]*Prime[# + 1] &]
%t PrimePi[#]&/@Select[Partition[Prime[Range[200]],3,1],#[[2]]^2<(#[[1]] #[[3]])&][[All,2]] (* _Harvey P. Dale_, Dec 09 2021 *)
%Y Cf. A046868, A000040.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 14 2013
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