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

Author

Hugo Pfoertner, Apr 01 2004

Keywords

• nonn
• look

Comments

Proposed by Leroy Quet, Mar 29 2004. Extended by R. K. Guy and Hugo Pfoertner.

Every odd prime occurs at least once at positions given by A005097.

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

Crossrefs

Cf. A005097, A000040, A093575, A093576.

Programs

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