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A184417 p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair. 1

%I

%S 33,73,289,649,1801,3529,7201,10369,20809,23329,38089,45001,64801,

%T 73729,78409,103969,115201,145801,159049,194689,242209,352801,373249,

%U 426889,544969,649801,720001,763849,824329,871201,1312201,1351369,1371169,1472329,1555849,2080801,2130049,2205001,2255689,2384929,2654209

%N p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair.

%C This seems to have a disproportionately high probability of generating a prime number.

%F Prime numbers in A063533 - 1.

%e a(1) = [prime(1)]^2 + [prime(1)+2]^2 - 1 = 3^2 + [3+2]^2 - 1 = 33

%e a(2) = [prime(2)]^2 + [prime(2)+2]^2 - 1 = 5^2 + [5+2]^2 - 1 = 73

%e a(3) = [prime(3)]^2 + [prime(3)+2]^2 - 1 = 11^2 + [11+2]^2 - 1 = 289

%t Total/@(Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&]^2)-1 (* _Harvey P. Dale_, Feb 24 2011 *)

%K nonn

%O 1,1

%A _Robert Mohr_, Feb 13 2011

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Last modified April 10 15:25 EDT 2021. Contains 342845 sequences. (Running on oeis4.)