A093574 Smallest prime of the form n^j+(n+1)^k, with j,k integer > 0.
3, 5, 7, 29, 11, 13, 71, 17, 19, 131, 23, 157, 2393, 29, 31, 83537, 307, 37, 419, 41, 43, 1013, 47, 601, 701, 53, 757, 615497, 59, 61, 1049537, 2113, 67, 1259, 71, 73, 1481, 1483, 79, 1721, 83, 3613, 1979, 89, 2161, 4977017, 2351, 97, 2549, 101, 103, 2861
Offset: 1
Examples
a(4)=29 because 4^1+5^2=29 is prime, whereas 4^1+5^1=9, 4^2+5=21 are composite.
Links
- Robert Israel, Table of n, a(n) for n = 1..825
Programs
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Maple
f:= proc(n) local t, pq; uses priqueue; initialize(pq); insert([-2*n-1,1,1],pq); do t:= extract(pq); if isprime(-t[1]) then return -t[1] fi; insert([-n^(t[2]+1)-(n+1)^t[3],t[2]+1,t[3]],pq); insert([-n^t[2]-(n+1)^(t[3]+1),t[2],t[3]+1],pq); od; end proc: map(f, [$1..60]); # Robert Israel, May 17 2024
Comments