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

1,2

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.

Links

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

Example

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.

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 #) &]

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), print1(n, ", ")))
(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

Crossrefs

Cf. A000040, A005098, A095278, A123986.

Sequence in context: A130052 A059255 A227024 * A022749 A036071 A225968

Adjacent sequences: A254373 A254374 A254375 * A254377 A254378 A254379

Keyword

nonn

Author

K. D. Bajpai, Jan 29 2015

Status

approved