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
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 12 2006
EXTENSIONS
More terms from Emeric Deutsch, Dec 24 2006
STATUS
approved