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%I #17 Jun 20 2016 11:15:42
%S 3,7,23,31,71,79,151,199,223,239,263,311,359,463,479,599,743,751,823,
%T 863,911,991,1031,1063,1103,1151,1303,1399,1471,1583,1759,1823,1831,
%U 1879,1999,2111,2143,2311,2383,2503,2543,2551,2663,2671,2719,3023,3079,3119,3191,3391,3511
%N Primes p such that (3/4)(p + 1) - 1 is also prime.
%C Set q = (3/4)(p + 1) - 1, then (q + 1)/(p + 1) = 3/4. If this sequence is proved to be infinite, that would prove two specific cases of the Schinzel-Sierpiński conjecture regarding rational numbers.
%C In fact this sequence is infinite under ('merely') Dickson's conjecture, as it requires infinitely many n with 3n + 2 and 4n + 3 both prime. - _Charles R Greathouse IV_, Apr 01 2016
%H G. C. Greubel, <a href="/A270384/b270384.txt">Table of n, a(n) for n = 1..1000</a>
%e 3 is in the sequence because 3/4 * 4 - 1 = 2, which is also prime.
%e 7 is in the sequence because 3/4 * 8 - 1 = 5, which is also prime.
%e 11 is not in the sequence because 3/4 * 12 - 1 = 8 = 2^3.
%t Select[Prime[Range[500]], PrimeQ[(3/4)(# + 1) - 1] &]
%o (PARI) is(n)=n%4==3 && isprime(n\4*3+2) && isprime(n) \\ _Charles R Greathouse IV_, Apr 01 2016
%Y Cf. A158721.
%K nonn
%O 1,1
%A _Alonso del Arte_, Mar 15 2016
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