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

1,1

Comments

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

Links

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

Example

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

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}]

Prog

(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

Crossrefs

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

Sequence in context: A291349 A293046 A213176 * A084443 A228029 A053711

Adjacent sequences: A236140 A236141 A236142 * A236144 A236145 A236146

Keyword

nonn

Author

Zhi-Wei Sun, Jan 19 2014

Status

approved