A188546 Numbers n such that m=(n^2+1)/2, p=(m^2+1)/2 and q=(p^2+1)/2 are all prime.

69, 271, 349, 3001, 3399, 4949, 6051, 9101, 9751, 10099, 10149, 11719, 12281, 15911, 22569, 24269, 25201, 25889, 28841, 31979, 37271, 39901, 42109, 44929, 46399, 48321, 50811, 60009, 63659, 63999, 71051, 71851, 75089, 76711, 87029, 96791, 103701, 110551, 111411, 112461, 113949, 125721, 126089, 127959, 129261, 131859, 132939, 137481, 144651

Offset: 1

Author

Zak Seidov, Apr 03 2011

Keywords

• nonn

Comments

a(1) = 69 = A116945(5).

Numbers n that generate three primes under the first three iterations of the map n-> A002731(n).

Subsequence of A116945.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002731, A105318, A116945, A188547, A187431.

Programs

Magma

r:=func< k | (k^2+1) div 2 >; [ n: n in [1..145000 by 2] | IsPrime(r(n)) and IsPrime(r(r(n))) and IsPrime(r(r(r(n)))) ];  // Bruno Berselli, Apr 05 2011

Mathematica

s={}; Do[If[PrimeQ[m=(n^2+1)/2] && PrimeQ[p=(m^2+1)/2] && PrimeQ[q=(p^2+1)/2], Print[n]; AppendTo[s,n]], {n,1,300000,2}]; s
mpqQ[n_]:=Module[{m=(n^2+1)/2,p},p=(m^2+1)/2;AllTrue[{m,p,(p^2+1)/2},PrimeQ]]; Select[Range[144700],mpqQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 18 2021 *)

PARI

v=vector(10^4);i=0;forstep(n=1,9e9,2,if(isprime(m=(n^2+1)/2)&isprime(p=(m^2+1)/2)&isprime(q=(p^2+1)/2),v[i++]=n;if(i==#v,return(v)))) \\ Charles R Greathouse IV, Apr 05 2011