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Smallest prime number of the form n^x+(n+1)^(x+1) where x >= 0.
1

%I #8 Sep 21 2024 08:42:39

%S 3,11,5,29,7,379,71,89,11,131,13,181,7900829,239,17,

%T 49814113380273715457,19,379,419,461,23,290489,599,404449,701,20359,

%U 29,431285689253609,31,991,1078367,56193275498055350689,5779302329076129802915210304491714273,1259,37,51949,1481,1559,41

%N Smallest prime number of the form n^x+(n+1)^(x+1) where x >= 0.

%C If x is allowed to be negative, then a(1) = 1^-1 + 2^0 = 2. - _Jason Yuen_, Sep 21 2024

%F a(n) = n^A130538(n) + (n+1)^(A130538(n)+1).

%e a(1) = 3 because x = 0 produces the prime 1^0+2^1 = 3;

%e a(16) = 49814113380273715457 because x < 15 produces composites and x = 15 produces the prime 16^15+17^16 = 49814113380273715457.

%o (PARI) a(n)=my(p);for(x=0,oo,p=n^x+(n+1)^(x+1);if(isprime(p),return(p))) \\ _Jason Yuen_, Sep 21 2024

%Y Cf. A130538.

%K nonn

%O 1,1

%A _Tomas Xordan_, Jun 02 2007