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A243528
Integers n such that p = 4n + 1, q = 4p + 3, r = 4q + 5, s = 4r + 7 and t = 4s + 9 are all prime.
1
1564, 4057, 4654, 5884, 26599, 30139, 37204, 66532, 74227, 80812, 98137, 113929, 124249, 138604, 245524, 249847, 250879, 299767, 309469, 315277, 340504, 346279, 359467, 362674, 367069, 401407, 410332, 435049, 437377, 438799, 537844, 550582, 579814, 587047
OFFSET
1,1
COMMENTS
The first prime n is 4057.
EXAMPLE
First 3 values of n, p, q, r, s and t:
{1564, 6257, 25031, 100129, 400523, 1602101},
{4057, 16229, 64919, 259681, 1038731, 4154933},
{4654, 18617, 74471, 297889, 1191563, 4766261}.
MATHEMATICA
pqrstQ[n_]:=Module[{p=4n+1, q, r, s}, q=4p+3; r=4q+5; s=4r+7; AllTrue[{p, q, r, s, 4s+9}, PrimeQ]]; Select[Range[590000], pqrstQ] (* Harvey P. Dale, Jan 18 2024 *)
PROG
(Magma) A141291:=func<h | (5*4^h-6*h-5) div 9>; [n: n in [1..10^6] | forall{i: i in [1..5] | IsPrime(4^i*n + A141291(i))}]; // Bruno Berselli, Jun 06 2014
CROSSREFS
Sequence in context: A031800 A280354 A072394 * A237673 A246734 A237467
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 06 2014
STATUS
approved