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A125855 Numbers k such that k+1, k+3, k+7 and k+9 are all primes. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A245304

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

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Last modified June 13 14:23 EDT 2021. Contains 345003 sequences. (Running on oeis4.)