A125855 Numbers k such that k+1, k+3, k+7 and k+9 are all primes.

4, 10, 100, 190, 820, 1480, 1870, 2080, 3250, 3460, 5650, 9430, 13000, 15640, 15730, 16060, 18040, 18910, 19420, 21010, 22270, 25300, 31720, 34840, 43780, 51340, 55330, 62980, 67210, 69490, 72220, 77260, 79690, 81040, 82720, 88810, 97840

Offset: 1

Author

Artur Jasinski, Dec 12 2006

Keywords

• nonn

Comments

It seems that, with the exception of 4, all terms are multiples of 10. - Emeric Deutsch, Dec 24 2006

In fact, all terms except 4 are congruent to 10 (mod 30). - Franklin T. Adams-Watters, Jun 05 2014

For n > 1: a(n) = 10*A007811(n-1). - Reinhard Zumkeller, Jul 18 2014 [Comment corrected by Jens Kruse Andersen, Jul 19 2014]

Examples

			For k = 10, the numbers 10 + 1 = 11, 10 + 3 = 13, 10 + 7 = 17, 10 + 9 = 19 are prime. - _Marius A. Burtea_, May 18 2019
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007530, A057015, A125779, A125780.

Cf. A010051, A245304 (subsequence), A007811.

Programs

Haskell

a125855 n = a125855_list !! (n-1)
a125855_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [1, 1, 1, 1]) [1, 3, 7, 9]
-- Reinhard Zumkeller, Jul 18 2014

Magma

[n:n in [1..100000]| IsPrime(n+1) and IsPrime(n+3) and IsPrime(n+7) and IsPrime(n+9)]; // Marius A. Burtea, May 18 2019

Maple

a:=proc(n): if isprime(n+1)=true and isprime(n+3)=true and isprime(n+7)=true and isprime(n+9)=true then n else fi end: seq(a(n),n=1..500000); # Emeric Deutsch, Dec 24 2006

Mathematica

Do[If[(PrimeQ[x + 1]) && (PrimeQ[x + 3]) && (PrimeQ[x + 7]) && (PrimeQ[x + 9]), Print[x]], {x, 1, 10000}]
(* Second program *)
Select[Range[10^5], Times @@ Boole@ Map[PrimeQ, # + {1, 3, 7, 9}] == 1 &] (* Michael De Vlieger, Jun 12 2017 *)
Select[Range[100000],AllTrue[#+{1,3,7,9},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 02 2018 *)

PARI

is(n) = my(v=[1, 3, 7, 9]); for(t=1, #v, if(!ispseudoprime(n+v[t]), return(0))); 1 \\ Felix Fröhlich, May 18 2019

Formula

a(n) = A007530(n) - 1. - R. J. Mathar, Jun 14 2017

Extensions

More terms from Emeric Deutsch, Dec 24 2006