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A254376 Numbers n such that 4n+1, 4n+3, 4n+7, 4n+9 and 4n+13 are prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 08:31 EST 2020. Contains 331293 sequences. (Running on oeis4.)