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A236119
Primes p with prime(p) - p - 1 and prime(p) - p + 1 both prime.
11
5, 17, 23, 41, 71, 83, 173, 293, 337, 353, 563, 571, 719, 811, 911, 953, 1201, 1483, 1579, 1877, 2081, 2089, 2309, 2579, 2749, 2803, 3329, 3343, 3511, 3691, 3779, 3851, 3881, 3907, 4021, 4049, 4093, 4657, 4813, 5051, 5179, 5333, 5519, 5591, 6053, 6547, 6841, 7151, 7723, 8209
OFFSET
1,1
COMMENTS
By the conjecture in A236097, this sequence should have infinitely many terms.
LINKS
EXAMPLE
a(1) = 5 since neither prime(2) - 2 - 1 = 0 nor prime(3) - 3 - 1 = 1 is prime, but prime(5) - 5 - 1 = 5 and prime(5) - 5 + 1 = 7 are both prime.
MATHEMATICA
p[n_]:=PrimeQ[Prime[n]-n-1]&&PrimeQ[Prime[n]-n+1]
n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1100}]
PROG
(PARI) s=[]; forprime(p=2, 10000, if(isprime(prime(p)-p-1) && isprime(prime(p)-p+1), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 19 2014
STATUS
approved