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A188546 Numbers n such that m=(n^2+1)/2, p=(m^2+1)/2 and q=(p^2+1)/2 are all prime. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)