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

1,2

Comments

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

Subsequence of A123986.

Links

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

Example

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.

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 #) &]

Prog

(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, ", ")))
(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

Crossrefs

Cf. A000040, A005098, A095278, A123986.

Sequence in context: A234985 A264895 A283359 * A281858 A037232 A165330

Adjacent sequences: A254285 A254286 A254287 * A254289 A254290 A254291

Keyword

nonn

Author

K. D. Bajpai, Jan 27 2015

Status

approved