A236075 Odd primes p with prime(2*p) - 2*prime(p) and prime(p) - 2*prime((p-1)/2) both prime.
5, 29, 79, 101, 103, 109, 353, 487, 821, 1367, 1811, 2111, 2593, 2617, 2939, 2969, 3001, 3659, 3727, 3877, 3911, 5347, 5779, 6481, 6959, 7121, 9059, 9649, 10007, 10099, 11299, 11311, 11827, 12343, 12511, 12539, 12589, 12689, 12923, 13781, 13967, 14249, 15859, 15923, 16363, 16889, 17321, 17683, 17881, 18181
Offset: 1
Keywords
Examples
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.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
PQ[n_]:=n>0&&PrimeQ[n] p[n_]:=PQ[Prime[2n]-2Prime[n]]&&PQ[Prime[n]-2*Prime[(n-1)/2]] n=0;Do[If[p[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,2,10^6}] -
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
Comments