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Numbers n such that p-n=p#-n#, where p=nextprime(n), n#=nextprime(square root of n), p#=nextprime(square root of p).
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%I #7 Dec 19 2021 11:25:13

%S 2207,5327,7919,12767,27887,39595,44519,54287,139127,160799,253007,

%T 299203,332923,351647,368447,383159,458327,502677,597525,619363,

%U 863039,908199,966285,994001,1079517,1247687,1261127,1442399,1530161,1559997

%N Numbers n such that p-n=p#-n#, where p=nextprime(n), n#=nextprime(square root of n), p#=nextprime(square root of p).

%t npQ[n_]:=Module[{p=NextPrime[n],p1,n1=NextPrime[Sqrt[n]]},p1= NextPrime[ Sqrt[p]];p-n==p1-n1]; Select[Range[156*10^4],npQ] (* _Harvey P. Dale_, Dec 19 2021 *)

%K easy,nonn

%O 1,1

%A _Naohiro Nomoto_