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

1,1

Comments

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

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A000040, A236074.

Sequence in context: A087348 A154412 A339935 * A272650 A050409 A111937

Adjacent sequences: A236072 A236073 A236074 * A236076 A236077 A236078

Keyword

nonn

Author

Zhi-Wei Sun, Jan 19 2014

Status

approved