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A235920
Primes p with prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) both prime.
1
17, 31, 41, 43, 61, 71, 83, 103, 109, 173, 181, 211, 271, 349, 353, 541, 661, 673, 743, 811, 911, 953, 971, 1171, 1429, 1471, 1483, 1723, 1787, 2053, 2203, 2579, 2749, 3019, 3299, 3391, 3433, 3463, 3727, 3917, 4003, 4021, 4049, 4243, 4447, 4567, 4657, 4729, 4801, 4993
OFFSET
1,1
COMMENTS
By the conjecture in A235919, this sequence should have infinitely many terms.
EXAMPLE
a(1) = 17 with prime(17) - 17 + 1 = 59 - 16 = 43 and (17^2 - 1)/4 - prime(17) = 72 - 59 = 13 both prime.
MATHEMATICA
PQ[n_]:=n>0&&PrimeQ[n]
p[n_]:=PrimeQ[Prime[n]-n+1]&&PQ[(n^2-1)/4-Prime[n]]
n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 17 2014
STATUS
approved