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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. 0

%I

%S 3727470,16547895,20983605,25649085,27563745,27906165,38221260,

%T 41232960,55136850,70584030,72097305,78362415,91531320,94746750,

%U 121155165,134647800,134660370,141473715,150940515,188741475,261431820,275356290,275952675,276220965,307341165,311631255

%N 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 For k = 134467800, 275356290 and 443034450, 2*k*(k+1) + 1 is also prime.

%o (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 Subsequence of A138303.

%K nonn

%O 1,1

%A _Pierre CAMI_, Mar 19 2008

%E Terms corrected by _Jinyuan Wang_, Mar 20 2020

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)