A093574 - OEIS

%I #18 May 18 2024 02:00:44

%S 3,5,7,29,11,13,71,17,19,131,23,157,2393,29,31,83537,307,37,419,41,43,

%T 1013,47,601,701,53,757,615497,59,61,1049537,2113,67,1259,71,73,1481,

%U 1483,79,1721,83,3613,1979,89,2161,4977017,2351,97,2549,101,103,2861

%N Smallest prime of the form n^j+(n+1)^k, with j,k integer > 0.

%C Proposed by _Leroy Quet_, Mar 29 2004. Extended by _R. K. Guy_ and _Hugo Pfoertner_.

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

%H Robert Israel, <a href="/A093574/b093574.txt">Table of n, a(n) for n = 1..825</a>

%e a(4)=29 because 4^1+5^2=29 is prime, whereas 4^1+5^1=9, 4^2+5=21 are composite.

%p f:= proc(n) local t, pq;

%p uses priqueue;

%p initialize(pq);

%p insert([-2*n-1,1,1],pq);

%p do

%p   t:= extract(pq);

%p   if isprime(-t[1]) then return -t[1] fi;

%p   insert([-n^(t[2]+1)-(n+1)^t[3],t[2]+1,t[3]],pq);

%p   insert([-n^t[2]-(n+1)^(t[3]+1),t[2],t[3]+1],pq);

%p od;

%p end proc:

%p map(f, [$1..60]); # _Robert Israel_, May 17 2024

%Y Cf. A005097, A000040, A093575, A093576.

%K nonn,look

%O 1,1

%A _Hugo Pfoertner_, Apr 01 2004