A125855 - OEIS

%I #35 Sep 08 2022 08:45:29

%S 4,10,100,190,820,1480,1870,2080,3250,3460,5650,9430,13000,15640,

%T 15730,16060,18040,18910,19420,21010,22270,25300,31720,34840,43780,

%U 51340,55330,62980,67210,69490,72220,77260,79690,81040,82720,88810,97840

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

%C It seems that, with the exception of 4, all terms are multiples of 10. - _Emeric Deutsch_, Dec 24 2006

%C In fact, all terms except 4 are congruent to 10 (mod 30). - _Franklin T. Adams-Watters_, Jun 05 2014

%C For n > 1: a(n) = 10*A007811(n-1). - _Reinhard Zumkeller_, Jul 18 2014 [Comment corrected by _Jens Kruse Andersen_, Jul 19 2014]

%H Reinhard Zumkeller, <a href="/A125855/b125855.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A007530(n) - 1. - _R. J. Mathar_, Jun 14 2017

%e 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

%p 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

%t Do[If[(PrimeQ[x + 1]) && (PrimeQ[x + 3]) && (PrimeQ[x + 7]) && (PrimeQ[x + 9]), Print[x]], {x, 1, 10000}]

%t (* Second program *)

%t Select[Range[10^5], Times @@ Boole@ Map[PrimeQ, # + {1, 3, 7, 9}] == 1 &] (* _Michael De Vlieger_, Jun 12 2017 *)

%t 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 *)

%o (Haskell)

%o a125855 n = a125855_list !! (n-1)

%o a125855_list = map (pred . head) $ filter (all (== 1) . map a010051') $

%o    iterate (zipWith (+) [1, 1, 1, 1]) [1, 3, 7, 9]

%o -- _Reinhard Zumkeller_, Jul 18 2014

%o (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

%o (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

%Y Cf. A007530, A057015, A125779, A125780.

%Y Cf. A010051, A245304 (subsequence), A007811.

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 12 2006

%E More terms from _Emeric Deutsch_, Dec 24 2006