A245304 Numbers m such that m+1, m+3, m+7, m+9 and m+13 are all primes.

4, 10, 100, 1480, 16060, 19420, 21010, 22270, 43780, 55330, 144160, 165700, 166840, 195730, 201820, 225340, 247600, 268810, 326140, 347980, 361210, 397750, 465160, 518800, 536440, 633460, 633790, 661090, 768190, 795790, 829720, 857950, 876010, 958540

Offset

1,1

References

W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970. Problem #82, variant.

Links

Reinhard Zumkeller and Jens Kruse Andersen, Table of n, a(n) for n = 1..1000 (first 120 terms from Zumkeller)

Formula

a(n) = A022006(n)-1. - Jens Kruse Andersen, Jul 18 2014

Mathematica

Select[Range[10^6], AllTrue[#+{1, 3, 7, 9, 13}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 07 2015 *)

Prog

(Haskell)
a245304 n = a245304_list !! (n-1)
a245304_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [1, 1, 1, 1, 1]) [1, 3, 7, 9, 13]
(PARI) forprime(p=2, 10^7, m=p-1; if(isprime(m+3)&&isprime(m+7)&&isprime(m+9)&&isprime(m+13), print1(m", "))) \\ Jens Kruse Andersen, Jul 18 2014
(Magma) [n: n in [0..10^6] | IsPrime(n+1) and IsPrime(n+3) and IsPrime(n+7) and IsPrime(n+9) and IsPrime(n+13)]; // Vincenzo Librandi, Jun 15 2015

Crossrefs

Cf. A010051, A022006, A245305, A007811, subsequence of A125855.

Sequence in context: A261842 A153743 A370987 * A298953 A197851 A197865

Adjacent sequences: A245301 A245302 A245303 * A245305 A245306 A245307

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2014

Status

approved