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.

3727470, 16547895, 20983605, 25649085, 27563745, 27906165, 38221260, 41232960, 55136850, 70584030, 72097305, 78362415, 91531320, 94746750, 121155165, 134647800, 134660370, 141473715, 150940515, 188741475, 261431820, 275356290, 275952675, 276220965, 307341165, 311631255

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..26.

Mathematica

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 *)

Prog

(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

Crossrefs

Subsequence of A138303.

Sequence in context: A328215 A216002 A187644 * A254496 A254489 A253861

Adjacent sequences: A136284 A136285 A136286 * A136288 A136289 A136290

Keyword

nonn

Author

Pierre CAMI, Mar 19 2008

Extensions

Terms corrected by Jinyuan Wang, Mar 20 2020

Status

approved