A254376 Numbers n such that 4n+1, 4n+3, 4n+7, 4n+9 and 4n+13 are prime.

1, 25, 370, 4015, 4855, 10945, 36040, 41425, 41710, 50455, 56335, 61900, 81535, 86995, 116290, 129700, 134110, 158365, 207430, 239635, 255625, 265990, 267175, 272815, 293395, 311590, 335080, 337810, 339700, 342115, 365350, 393385, 403960, 481345, 488590, 550990

Offset: 1

Author

K. D. Bajpai, Jan 29 2015

Keywords

• nonn

Comments

All terms in this sequence are 1 mod 3.

Each term yields a set of five consecutive primes.

Alternatively: Numbers n such that 4n+k forms a set of five consecutive primes for k = {1,3,7,9,13}.

Subsequence of A123986.

Examples

			25 is in the list because 4*25 + 1 = 101, 4*25 + 3 = 103, 4*25 + 7 = 107, 4*25 + 9 = 109 and 4*25 + 13 = 113 are all prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..8458

Crossrefs

Cf. A000040, A005098, A095278, A123986.

Programs

Magma

[n: n in [0..10^6] | forall{4*n+r: r in [1,3,7,9,13] | IsPrime(4*n+r)}]; // Vincenzo Librandi, Feb 16 2015

Mathematica

Select[Range[1, 500000], PrimeQ[4*# + 1] && PrimeQ[4*# + 3] && PrimeQ[4*# + 7] && PrimeQ[4*# + 9] && PrimeQ[4*# + 13] &]
Select[Range[5*10^6], And @@ PrimeQ /@ ({1, 3, 7, 9, 13} + 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), print1(n,", ")))