A138303 -id:A138303 - 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, 2k(k+1) - 1, 2k(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

Pierre CAMI, Mar 19 2008

nonn

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

Subsequence of A138303.

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 *)

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

Terms corrected by Jinyuan Wang, Mar 20 2020

A138301 Number of integers k < 10^n such that k(k+1)-1 and k(k+3)-1 are both first of twin primes.

Original entry on oeis.org

1, 2, 4, 11, 37, 145, 673, 3748, 22875

Offset: 1

Pierre CAMI, Mar 14 2008

nonn

			3*4-1=11 11 and 13 twin primes, 3*6-1=17 17 and 19 twin primes a(1)=1
15*16-1=239 239 and 241 twin primes, 15*18-1=269 269 and 271 twin primes a(2)=2

Cf. A138303.

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, 2k(k+1) - 1, 2k(k+3) - 1 are all primes.

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A138301 Number of integers k < 10^n such that k(k+1)-1 and k(k+3)-1 are both first of twin primes.

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Author

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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.

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Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Extensions

A138301 Number of integers k < 10^n such that k*(k+1)-1 and k*(k+3)-1 are both first of twin primes.

Views

Author

Keywords

Examples

Crossrefs

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, 2k(k+1) - 1, 2k(k+3) - 1 are all primes.

A138301 Number of integers k < 10^n such that k(k+1)-1 and k(k+3)-1 are both first of twin primes.