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

1,1

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A115920 A183447 A296126 * A158732 A069216 A158736

Adjacent sequences: A188543 A188544 A188545 * A188547 A188548 A188549

Keyword

nonn

Author

Zak Seidov, Apr 03 2011

Status

approved