A136287 - OEIS

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

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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.

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