A243528 Integers n such that p = 4n + 1, q = 4p + 3, r = 4q + 5, s = 4r + 7 and t = 4s + 9 are all prime.

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.

Links

Table of n, a(n) for n=1..34.

Zak Seidov, Table of first 30 values of n, p, q, r, s, t.

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

Adjacent sequences: A243525 A243526 A243527 * A243529 A243530 A243531

Keyword

nonn

Author

Zak Seidov, Jun 06 2014

Status

approved