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%I #30 Sep 08 2022 08:45:56
%S 4949,6051,169219,183241,560769,1113621,1306689,1370269,1421869,
%T 1485561,1640711,1730709,1876351,1967769,2147661,2217351,2293939,
%U 2428461,2440871,3346661,3625139,3625889,3763969,3991209,4020711,4728141,5219691,5547221,5554939,5965699,7345719,8495879
%N Numbers n such that m=(n^2+1)/2, p=(m^2+1)/2, q=(p^2+1)/2, and r=(q^2+1)/2 are all prime.
%C a(1) = 4949 = A188546(6) = A116945(53).
%C Subsequence of A188546.
%C Numbers n which generate 4 primes under the first four iterations of the map n-> A002731(n).
%C Among first 10000 terms, there are 1072 primes, the first a(3) = 169219 and the last a(10000) = 16541600731. - _Zak Seidov_, Jan 16 2019
%H Charles R Greathouse IV, <a href="/A188547/b188547.txt">Table of n, a(n) for n = 1..10000</a>, replacing an earlier file from Zak Seidov
%t s={}; Do[If[PrimeQ[m=(n^2+1)/2] && PrimeQ[p=(m^2+1)/2] && PrimeQ[q=(p^2+1)/2] && PrimeQ[r=(q^2+1)/2], AppendTo[s,n]], {n,1,10000000,2}]; s
%o (PARI) v=vector(10^4); i=0; forstep(n=1, 9e99, 2, if(isprime(m=(n^2+1)/2) && isprime(p=(m^2+1)/2) && isprime(q=(p^2+1)/2) && isprime(r=(q^2+1)/2), v[i++]=n; if(i==#v, return))) \\ _Charles R Greathouse IV_, Apr 12 2011
%o (Magma) r:=func< k | (k^2+1) div 2 >; [ n: n in [1..1000000 by 2] | IsPrime(r(n)) and IsPrime(r(r(n))) and IsPrime(r(r(r(n))))and IsPrime(r(r(r(r(n)))))]; // _Vincenzo Librandi_, Jan 16 2019
%Y Cf. A002731, A105318, A116945, A188546, A187431.
%K nonn
%O 1,1
%A _Zak Seidov_, Apr 03 2011
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