A236143 Odd primes p with prime(p-1) - (p-1) and prime(p-1) - 2*prime((p-1)/2) both prime.

7, 11, 31, 67, 179, 193, 197, 281, 347, 349, 563, 599, 757, 1123, 1453, 1543, 1933, 1987, 2083, 2531, 2971, 3037, 3259, 3547, 3583, 3701, 3919, 4027, 4483, 5023, 5581, 5591, 5647, 5981, 6449, 7207, 7297, 7603, 8291, 9049

Offset: 1

Author

Zhi-Wei Sun, Jan 19 2014

Keywords

• nonn

Comments

By part (i) of the conjecture in A236138, this sequence should have infinitely many terms.

Examples

			a(1) = 7 with prime(6) - 6 = 13 - 6 = 7 and prime(6) - 2*prime(3) = 13 - 2*5 = 3 both prime.
		

Links

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

Crossrefs

Cf. A000040, A234695, A235925, A236075, A236119, A236138.

Programs

Mathematica

PQ[n_]:=n>0&&PrimeQ[n]
p[n_]:=PrimeQ[Prime[n-1]-(n-1)]&&PQ[Prime[n-1]-2*Prime[(n-1)/2]]
n=0;Do[If[p[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,2,10^5}]

PARI

s=[]; forprime(p=3, 10000, if(isprime(prime(p-1)-(p-1)) && isprime(prime(p-1)-2*prime((p-1)/2)), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014