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A093574 Smallest prime of the form n^j+(n+1)^k, with j,k integer > 0.

%I A093574 #18 May 18 2024 02:00:44
%S A093574 3,5,7,29,11,13,71,17,19,131,23,157,2393,29,31,83537,307,37,419,41,43,
%T A093574 1013,47,601,701,53,757,615497,59,61,1049537,2113,67,1259,71,73,1481,
%U A093574 1483,79,1721,83,3613,1979,89,2161,4977017,2351,97,2549,101,103,2861
%N A093574 Smallest prime of the form n^j+(n+1)^k, with j,k integer > 0.
%C A093574 Proposed by _Leroy Quet_, Mar 29 2004. Extended by _R. K. Guy_ and _Hugo Pfoertner_.
%C A093574 Every odd prime occurs at least once at positions given by A005097.
%H A093574 Robert Israel, <a href="/A093574/b093574.txt">Table of n, a(n) for n = 1..825</a>
%e A093574 a(4)=29 because 4^1+5^2=29 is prime, whereas 4^1+5^1=9, 4^2+5=21 are composite.
%p A093574 f:= proc(n) local t, pq;
%p A093574 uses priqueue;
%p A093574 initialize(pq);
%p A093574 insert([-2*n-1,1,1],pq);
%p A093574 do
%p A093574   t:= extract(pq);
%p A093574   if isprime(-t[1]) then return -t[1] fi;
%p A093574   insert([-n^(t[2]+1)-(n+1)^t[3],t[2]+1,t[3]],pq);
%p A093574   insert([-n^t[2]-(n+1)^(t[3]+1),t[2],t[3]+1],pq);
%p A093574 od;
%p A093574 end proc:
%p A093574 map(f, [$1..60]); # _Robert Israel_, May 17 2024
%Y A093574 Cf. A005097, A000040, A093575, A093576.
%K A093574 nonn,look
%O A093574 1,1
%A A093574 _Hugo Pfoertner_, Apr 01 2004