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

Author

Reinhard Zumkeller, Jul 18 2014

Keywords

• nonn

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)

Crossrefs

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

Programs

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]

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

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 *)

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

Formula

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