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%I #14 Aug 18 2019 02:33:00
%S 4,6,10,11,14,16,17,20,22,24,26,28,30,31,36,38,39,40,45,48,50,52,54,
%T 56,57,59,62,65,66,67,70,73,74,76,79,81,84,85,87,90,91,94,95,96,97,99,
%U 100,104,105,106,109,110,111,114,115,116,120,122,123,124,125,126,130,134
%N Numbers n such that n^2 > (1/2)(prevprime(n^2)+nextprime(n^2)).
%C One may call these n^2 the "strong squares" by analogy with A051634 (Strong primes).
%e 4^2=16>(13+17)/2 so 4 is a term;
%e 5^2 < (23+29)/2=26, so 5 is not a term;
%e 6^2=36>(31+37)/2 so 6 is a term, etc.
%p a:=proc(n) if n^2 > (1/2)*(prevprime(n^2)+nextprime(n^2)) then n else fi end: seq(a(n),n=2..150); # _Emeric Deutsch_, Jun 26 2005
%t prQ[n_]:=Module[{n2=n^2},n2>(NextPrime[n2]+NextPrime[n2,-1])/2]; Select[ Range[2,150],prQ] (* _Harvey P. Dale_, Feb 19 2012 *)
%Y Cf. A051634, A033597, A075190, A109269. The interprimes (the average of two consecutive odd primes) are in A024675.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 24 2005
%E More terms from _Emeric Deutsch_, Jun 26 2005
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