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

1,1

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]

Links

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

Formula

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A007530, A057015, A125779, A125780.

Cf. A010051, A245304 (subsequence), A007811.

Sequence in context: A156329 A266839 A203179 * A261842 A153743 A370987

Adjacent sequences: A125852 A125853 A125854 * A125856 A125857 A125858

Keyword

nonn

Author

Artur Jasinski, Dec 12 2006

Extensions

More terms from Emeric Deutsch, Dec 24 2006

Status

approved