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A090117 a(n) = x^2 = A090116(n)^2 is the least square that is "surrounded" by two closest primes, by prevprime(x^2) and nextprime(x^2) whose difference nextprime - prevprime = 2n.

%I A090117 #21 Apr 28 2019 20:07:15
%S A090117 4,9,25,361,144,625,121,1936,529,900,3249,1681,2500,10404,5776,10816,
%T A090117 10000,22201,30625,25281,121104,76176,93025,157609,212521,35721,
%U A090117 119025,1121481,190969,672400,693889,1004004,259081,1646089,675684,1207801
%N A090117 a(n) = x^2 = A090116(n)^2 is the least square that is "surrounded" by two closest primes, by prevprime(x^2) and nextprime(x^2) whose difference nextprime - prevprime = 2n.
%H A090117 Vincenzo Librandi, <a href="/A090117/b090117.txt">Table of n, a(n) for n = 1..57</a>
%e A090117 n=5: a(5)=144, primes closest to 144 are {139,149} of which the difference 149 - 139 = 10 = 2n and 144 is the smallest square with this property;
%e A090117 n=1: a(1)=4, 2^2 = 4 is surrounded by {3,5} closest primes with difference 5 - 3 = 2 = 2n.
%t A090117 de[x_ ]:= Prime[PrimePi[x]+1]-Prime[PrimePi[x]] t=Table[de[w^2], {w, 1, 50000}]; q=Table[Min[Flatten[Position[t, 2*j]]]^2, {j, 1, 100}]
%t A090117 Table[Min[Transpose[Select[{#,NextPrime[#]-NextPrime[#,-1]}&/@ (Range[ 2,5000]^2), Last[#]==2n&]][[1]]],{n,40}] (* _Harvey P. Dale_, Sep 04 2011 *)
%Y A090117 Cf. A090116, A090117, A090118, A090119.
%K A090117 nonn
%O A090117 1,1
%A A090117 _Labos Elemer_, Jan 09 2004