A254288 Numbers k such that 4*k + {1, 3, 7, 9, 13, 19} are all prime.

1, 370, 41425, 81535, 255625, 267175, 311590, 365350, 1054570, 1381750, 2533600, 2975125, 3266080, 3930205, 4684210, 4782385, 4802860, 5940850, 6414610, 7986565, 8429245, 8570470, 8636305, 8810080, 9270715, 9857980, 10459525, 13708225, 13917490, 15127720, 15252460

Offset: 1

Author

K. D. Bajpai, Jan 27 2015

Keywords

• nonn

Comments

All terms in this sequence are congruent to 1 mod 3.

Subsequence of A123986.

Examples

			a(2) = 370;
4*370 +  1 = 1481;
4*370 +  3 = 1483;
4*370 +  7 = 1487;
4*370 +  9 = 1489;
4*370 + 13 = 1493;
4*370 + 19 = 1499;
All six are prime.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 726 terms from K. D. Bajpai)

Crossrefs

Cf. A000040, A005098, A095278, A123986.

Programs

Magma

[n: n in [0..10^8] | forall{4*n+i: i in [1, 3, 7, 9, 13, 19] |  IsPrime(4*n+i)}]; // Vincenzo Librandi, Mar 12 2015

Mathematica

Select[Range[5*10^7], PrimeQ[4*# + 1] && PrimeQ[4*# + 3] && PrimeQ[4*# + 7] && PrimeQ[4*# + 9] && PrimeQ[4*# + 13] && PrimeQ[4*# + 19] &]
Select[Range[5*10^6], And @@ PrimeQ /@ ({1, 3, 7, 9, 13, 19} + 4 #) &]

PARI

for(n=1,10^7, if( isprime(4*n + 1) && isprime(4*n + 3) &&isprime(4*n + 7) &&isprime(4*n + 9) &&isprime(4*n + 13) &&isprime(4*n + 19) , print1(n,", ")))