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%I #25 Sep 10 2023 21:55:11
%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 a(n) = A063533(n) - 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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