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 A231735 #48 May 28 2025 19:22:52
%S A231735 2,2,1,1,2,1,1128,1,0,3,2,1,6,1,2,3,2,1,6,1,2,3,14,1,0,2,2,6,206,1,
%T A231735 1590,1,2,11,2,3
%N A231735 Least positive k such that n*k^k - 1 is a prime, or 0 if no such k exists.
%C A231735 From _Gordon Atkinson_, Aug 20 2019: (Start)
%C A231735 For all odd numbers n > 3, a(n) is even.
%C A231735 For all odd numbers n > 1, a(n^2) = 0. (End)
%C A231735 a(37) > 10^4. - _Jinyuan Wang_, Mar 05 2020
%C A231735 From _Kevin P. Thompson_, Feb 12 2023: (Start)
%C A231735 Other known terms: a(38) = 1, a(39) = 6, a(40) = 6, a(41) = 2, a(42) = 1, a(44) = 8, a(45) = 22, a(47) = 48, a(48) = 7, a(49) = 0, a(50) = 14.
%C A231735 Other unknown terms: a(43) > 5000, a(46) > 1000, a(51) > 1000. (End)
%C A231735 a(37) > 10^5, a(43) > 10^5, a(46) = 5430, a(51) = 4010. - _Jason Yuen_, Jan 19 2025
%C A231735 a(37) > 150000, a(43) > 323000. - _Phillip Poplin_, May 28 2025
%F A231735 a(A008864(k)) = 1. - _Gordon Atkinson_, Sep 04 2019
%e A231735 The least k > 0 such that 5*k^k - 1 is a prime is k = 2, so a(5) = 2.
%t A231735 Table[If[And[n > 1, OddQ@ Sqrt@ n], 0, If[And[n > 3, OddQ@ n], Block[{k = 2}, While[! PrimeQ[n*k^k - 1], k += 2]; k], Block[{k = 1}, While[! PrimeQ[n*k^k - 1], k++]; k]]], {n, 36}] (* _Michael De Vlieger_, Sep 29 2019 *)
%o A231735 (PARI) a(n) = if(sqrt(n)%2==1 && n>1, 0, for(k=1, oo, if(ispseudoprime(n*k^k-1), return(k)))); \\ _Jinyuan Wang_, Mar 05 2020
%Y A231735 Cf. A000040, A008864, A193807, A231734.
%K A231735 nonn,hard,more
%O A231735 1,1
%A A231735 _Alex Ratushnyak_, Nov 12 2013
%E A231735 a(9) and a(25) from _Gordon Atkinson_, Aug 20 2019
%E A231735 a(26)-a(36) from _Alois P. Heinz_, Aug 20 2019