A236075 - OEIS

%I #8 Jan 19 2014 04:44:33

%S 5,29,79,101,103,109,353,487,821,1367,1811,2111,2593,2617,2939,2969,

%T 3001,3659,3727,3877,3911,5347,5779,6481,6959,7121,9059,9649,10007,

%U 10099,11299,11311,11827,12343,12511,12539,12589,12689,12923,13781,13967,14249,15859,15923,16363,16889,17321,17683,17881,18181

%N Odd primes p with prime(2*p) - 2*prime(p) and prime(p) - 2*prime((p-1)/2) both prime.

%C By the conjecture in A236074, this sequence should have infinitely many terms.

%H Zhi-Wei Sun, <a href="/A236075/b236075.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 5 since neither prime(2*2) - 2*prime(2) = 1 nor  prime(3) - 2*prime((3-1)/2) = 1 is prime, but prime(2*5) - 2*prime(5) = 29 - 2*11 = 7 and prime(5) - 2*prime((5-1)/2) = 11 - 2*3 = 5 are both prime.

%t PQ[n_]:=n>0&&PrimeQ[n]

%t p[n_]:=PQ[Prime[2n]-2Prime[n]]&&PQ[Prime[n]-2*Prime[(n-1)/2]]

%t n=0;Do[If[p[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,2,10^6}]

%o (PARI) s=[]; forprime(p=3, 20000, if(isprime(prime(2*p)-2*prime(p)) && isprime(prime(p)-2*prime((p-1)/2)), s=concat(s, p))); s \\ _Colin Barker_, Jan 19 2014

%Y Cf. A000040, A236074.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 19 2014