login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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