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 A086685 #16 May 17 2021 18:17:56
%S A086685 0,1,1,2,1,4,2,2,3,5,3,6,4,5,5,5,3,10,2,6,6,9,4,9,5,9,7,11,4,17,3,10,
%T A086685 9,12,9,15,4,9,11,13,5,21,7,11,10,16,8,19,6,18,13,17,5,23,10,18,9,16,
%U A086685 8,27,7,15,13,16,13,29,9,18,13,27,9,26,10,19,18,17,11,29,11,23,18,22,11,32
%N A086685 Number of 1 <= i < n such that i*n+1 is prime.
%C A086685 Number of primes p < n^2 such that p == 1 (mod n). The standard conjecture here is that a(n) ~ n^2/(2 phi(n)log n), where Euler's totient function phi(n) = A000010(n). - _Thomas Ordowski_, Oct 21 2014
%C A086685 Number of primes appearing in the 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - _Wesley Ivan Hurt_, May 17 2021
%F A086685 a(n) = Sum_{k=1..n} pi(1+n*(k-1)) - pi(n*(k-1)), where pi is the prime counting function. - _Wesley Ivan Hurt_, May 17 2021
%e A086685 For n=10, i=1,3,4,6,7 give primes, so a(10)=5.
%t A086685 f[n_] := Length[ Select[ Range[n - 1], PrimeQ[n# + 1] & ]]; Table[ f[n], {n, 1, 85}]
%t A086685 Table[Count[Range[n-1]n+1,_?PrimeQ],{n,90}] (* _Harvey P. Dale_, Oct 10 2013 *)
%o A086685 (PARI) nphi(n)=local(c); c=0; for (i=1,n-1,if (isprime(i*n+1),c++)); c for(i=1,60,print1(","nphi(i)))
%Y A086685 Cf. A000010 (phi), A000720 (pi).
%K A086685 nonn
%O A086685 1,4
%A A086685 _Jon Perry_, Jul 28 2003
%E A086685 Extended by _Robert G. Wilson v_, Jul 31 2003