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%I #16 Apr 12 2018 17:08:24
%S 3,1628779,2481113,3260683,3520229,9733123,10671253,10673129,11772809,
%T 36758303,45459353,45594019,58552279,64597903,66539353,74674559,
%U 83471243,96765313,115623929,117479039,131701183,133500553,145010533,163341319,163845719,166410353,167197243,169948223
%N Primes p such that f(p), f(f(p)), f(f(f(p))), and f(f(f(f(p)))) are all prime, where f(x) = x^2+3x+1.
%e p = 3, f(p) = 19, f(19) = 419, f(419) = 176819 , and f(176819) = 31265489219 all prime.
%t Select[Prime[Range[10^7]],AllTrue[Rest[NestList[#^2+3#+1&,#,4]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 12 2018 *)
%Y Subsequence of A250027. Cf. A094210, A153590.
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 11 2014