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A237414
Primes p with p^2 - 2 and prime(p)^2 - 2 both prime.
3
2, 3, 43, 47, 107, 139, 191, 211, 223, 239, 293, 313, 337, 541, 743, 757, 863, 1013, 1153, 1231, 1619, 2113, 2137, 2287, 2297, 2423, 2543, 2729, 2749, 2897, 3079, 3089, 3313, 3863, 3947, 4241, 4271, 4583, 4649, 4993, 5581, 6571, 6637, 6911, 7547, 8629, 8849, 8867, 9049, 9661
OFFSET
1,1
COMMENTS
According to the conjecture in A237413, this sequence should have infinitely many terms.
LINKS
EXAMPLE
a(1) = 2 since 2^2 - 2 = 2 and prime(2)^2 - 2 = 3^2 - 2 = 7 are both prime.
MATHEMATICA
p[n_]:=PrimeQ[n^2-2]
n=0; Do[If[p[Prime[k]]&&p[Prime[Prime[k]]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]
Select[Prime[Range[1200]], AllTrue[{#^2-2, Prime[#]^2-2}, PrimeQ]&] (* Harvey P. Dale, Apr 06 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 07 2014
STATUS
approved