A130537 - OEIS

A130537

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

3, 11, 5, 29, 7, 379, 71, 89, 11, 131, 13, 181, 7900829, 239, 17, 49814113380273715457, 19, 379, 419, 461, 23, 290489, 599, 404449, 701, 20359, 29, 431285689253609, 31, 991, 1078367, 56193275498055350689, 5779302329076129802915210304491714273, 1259, 37, 51949, 1481, 1559, 41

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OFFSET

1,1

COMMENTS

If x is allowed to be negative, then a(1) = 1^-1 + 2^0 = 2. - Jason Yuen, Sep 21 2024

LINKS

Table of n, a(n) for n=1..39.

FORMULA

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

EXAMPLE

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

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