cp's OEIS Frontend

A136287 Numbers k such that k*(k+1) - 1 and k*(k+3) - 1 are both the initial member of a pair of twin primes and Sophie Germain primes. In other words, k*(k+1) - 1, k*(k+1) + 1, k*(k+3) - 1, k*(k+3) + 1, 2*k*(k+1) - 1, 2*k*(k+3) - 1 are all primes.

%I A136287 #9 Mar 05 2025 18:10:52
%S A136287 3727470,16547895,20983605,25649085,27563745,27906165,38221260,
%T A136287 41232960,55136850,70584030,72097305,78362415,91531320,94746750,
%U A136287 121155165,134647800,134660370,141473715,150940515,188741475,261431820,275356290,275952675,276220965,307341165,311631255
%N A136287 Numbers k such that k*(k+1) - 1 and k*(k+3) - 1 are both the initial member of a pair of twin primes and Sophie Germain primes. In other words, k*(k+1) - 1, k*(k+1) + 1, k*(k+3) - 1, k*(k+3) + 1, 2*k*(k+1) - 1, 2*k*(k+3) - 1 are all primes.
%C A136287 For k = 134467800, 275356290 and 443034450, 2*k*(k+1) + 1 is also prime.
%t A136287 Select[Range[28*10^6],AllTrue[{#(#+1)-1,#(#+1)+1,#(#+3)-1,#(#+3)+1,2#(#+1)-1,2#(#+3)-1},PrimeQ]&] (* The program generates the first six terms of the sequence. *) (* _Harvey P. Dale_, Mar 05 2025 *)
%o A136287 (PARI) is(k) = !(k%15) && isprime(k*(k+1)-1) && isprime(k*(k+1)+1) && isprime(k*(k+3)-1) && isprime(k*(k+3)+1) && isprime(2*k*(k+1)-1) && isprime(2*k*(k+3)-1); \\ _Jinyuan Wang_, Mar 20 2020
%Y A136287 Subsequence of A138303.
%K A136287 nonn
%O A136287 1,1
%A A136287 _Pierre CAMI_, Mar 19 2008
%E A136287 Terms corrected by _Jinyuan Wang_, Mar 20 2020