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Both 1 + 6 n and 6 + 35 n are prime.
1

%I #18 Sep 08 2022 08:46:07

%S 1,5,7,13,17,23,25,35,37,55,61,91,95,101,121,131,137,143,161,175,187,

%T 221,233,245,257,271,311,335,391,395,397,443,445,451,461,475,511,527,

%U 545,557,577,583,641,653,683,685,703,737,761,773,787,797,805

%N Both 1 + 6 n and 6 + 35 n are prime.

%C The consecutive integers 35 + 210 a(n) and 36 + 210 a(n) are both products of three primes (distinct if n > 1).

%H Robert Israel, <a href="/A240716/b240716.txt">Table of n, a(n) for n = 1..10000</a>

%p A240716 := select(t -> andmap(isprime,[1+6*t,6+35*t]),[$1..N]); # _Robert Israel_, Apr 10 2014

%t Select[Range[1000], PrimeQ[6 # + 1] && PrimeQ[35 # + 6] &] (* _Vincenzo Librandi_, Jul 01 2014 *)

%o (Magma) [n: n in [0..1000] | IsPrime(6*n+1) and IsPrime(35*n+6)]; // _Vincenzo Librandi_, Jul 01 2014

%Y Cf. A215217.

%K nonn

%O 1,2

%A _Robert Israel_, Apr 10 2014