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

1,1

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.

Links

Robert Israel, Table of n, a(n) for n = 1..825

Example

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

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

Crossrefs

Cf. A005097, A000040, A093575, A093576.

Sequence in context: A352106 A061944 A288924 * A076846 A046931 A154551

Adjacent sequences: A093571 A093572 A093573 * A093575 A093576 A093577

Keyword

nonn,look

Author

Hugo Pfoertner, Apr 01 2004

Status

approved