This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180362 #17 Jul 28 2025 12:17:26
%S A180362 5,13,109,163,257,271,379,433,487,541,769,3329,7681,7937,9473,10753,
%T A180362 11777,12289,13313,14081,14593,15361,17921,18433,19457,22273,23041,
%U A180362 23297,25601,26113,26881,30977,31489,32257,36097,36353,37501,37633,37889,39937,40193
%N A180362 Primes of the form k * m^m + 1 with k < m^m.
%C A180362 A result of Heath-Brown shows, on the GRH, that this sequence is infinite; can this be proved unconditionally? The averaged result of Bombieri-Friedlander-Iwaniec does not seem to be strong enough.
%H A180362 Charles R Greathouse IV, <a href="/A180362/b180362.txt">Table of n, a(n) for n = 1..10000</a>
%H A180362 D. R. Heath-Brown, <a href="https://web.archive.org/web/20160317102203/http://eprints.maths.ox.ac.uk/166/1/linnik.pdf">Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression</a>, Proceedings of the London Mathematical Society 64:3 (1992), pp. 265-338.
%F A180362 k * m^m + 1, where k < m^m.
%e A180362 a(4) = 109, because 4 * 3^3 + 1 = 109, which is prime, and 4 < 27.
%t A180362 Take[Select[Union[Flatten[Table[k m^m+1,{m,5},{k,m^m-1}]]],PrimeQ],50] (* _Harvey P. Dale_, Jul 28 2025 *)
%o A180362 (PARI) isA180362(n)=my(b=2);while(b^b<n,if(n%(b^b)==1 && n < b^(2*b), return(isprime(n)));b++);0
%K A180362 nonn
%O A180362 1,1
%A A180362 Kevin Batista (kevin762401(AT)yahoo.com), Aug 30 2010, Sep 01 2010
%E A180362 Edited by _Charles R Greathouse IV_, Sep 01 2010