A075705 Safe primes (A005385) (p and (p-1)/2 are primes) such that 6*p+1 is also prime.

5, 7, 11, 23, 47, 83, 107, 263, 347, 467, 503, 863, 887, 1283, 1487, 1823, 1907, 2027, 2063, 2447, 2903, 3203, 3623, 4007, 4127, 4547, 4703, 4787, 5387, 5807, 7523, 7703, 8147, 8423, 11423, 11483, 11807, 12107, 12227, 12647, 12983, 13043, 13163, 14087, 14207

Offset

1,1

Links

David Consiglio, Jr. and T. D. Noe, Table of n, a(n) for n = 1..1000

Example

47 is prime, so is (47-1)/2=23 and also 6*47+1=283; 83 is a prime, (83-1)/2=41 and 6*83+1=499, ...

Maple

ts_sg_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_sg_var_pras(i), i=1..3000);

Mathematica

Select[Range[20000], PrimeQ[#] && PrimeQ[(#-1)/2] && PrimeQ[6#+1] &] (* T. D. Noe, Nov 07 2011 *)
Select[Prime[Range[1700]], And@@PrimeQ[{(#-1)/2, 6#+1}]&] (* Harvey P. Dale, Feb 28 2013 *)

Crossrefs

Cf. A005384, A005385, A059455, A007693.

Sequence in context: A092307 A005385 A181602 * A340308 A339096 A249735

Adjacent sequences: A075702 A075703 A075704 * A075706 A075707 A075708

Keyword

nonn

Author

Jani Melik, Oct 02 2002

Status

approved