A075706 Safe primes (A005385) (p and (p-1)/2 are primes) such that 8*p+1 (A023228) is also prime.

5, 11, 107, 179, 347, 479, 1187, 1307, 1367, 1487, 1619, 2027, 2207, 2447, 2999, 3119, 3467, 4007, 4079, 4139, 4799, 5087, 5807, 5927, 5939, 6827, 7079, 7247, 8699, 9587, 9839, 10607, 12107, 12539, 12659, 14207, 15299, 16139, 16187, 17027

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

11 is a prime, so is (11-1)/2=5 and also 8*11+1=89; 107 is a prime, (107-1)/2=53 and 8*107+1=857, ...

Maple

ts_sg8_var_pras := proc(nmax) local i, tren, atek; tren := 0: for i from 1 to nmax do atek := numtheory[safeprime](i): if (atek > tren) then if (isprime(atek)='true' and isprime(6*atek+1)='true') then tren := atek: fi; fi; od; end: seq(ts_sg8_var_pras(i), i=1..3000);

Mathematica

Select[Prime[Range[2000]], AllTrue[{(#-1)/2, 8#+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 31 2020 *)

Prog

(PARI) forprime(p=3, 20000, if(isprime((p-1)/2), if(isprime(8*p+1), print1(p", "))))

Crossrefs

Cf. A005384, A005385, A059455, A023228.

Sequence in context: A056111 A090160 A062652 * A338083 A236509 A330488

Adjacent sequences: A075703 A075704 A075705 * A075707 A075708 A075709

Keyword

nonn

Author

Jani Melik, Oct 02 2002

Extensions

More terms from Ralf Stephan, Mar 19 2003

Status

approved