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 A338558 #45 Jan 10 2025 04:34:28
%S A338558 0,0,0,0,1,5,7,7,1,5,10,6,11,12,20,24,14,12,3,19,6,37,20,33,20,27,50,
%T A338558 34,36,29,18,64,4,2,66,32,3,64,61,51,60,84,95,83,63,97,42,28,61,67,32,
%U A338558 10,29,73,37,92,16,120,31,107,120,141,145,39,12,74,150
%N A338558 Absolute value q such that tau(p) == q (mod p), where p = prime(n) and tau(i) = A000594(i).
%C A338558 These are essentially the values that can be used to define "near-misses" in a search of terms for A007659, similar to how "near-Wieferich primes", "near-Wilson primes" and "near-Wall-Sun-Sun primes" are defined in searches for Wieferich primes (A001220), Wilson primes (A007540) and Wall-Sun-Sun (Fibonacci-Wieferich) primes.
%H A338558 Amiram Eldar, <a href="/A338558/b338558.txt">Table of n, a(n) for n = 1..10000</a>
%H A338558 Nik Lygeros and Olivier Rozier, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Lygeros/lygeros5.html">A new solution for the equation tau(p)=0 (mod p)</a>, Journal of Integer Sequences 13 (2010), Article 10.7.4.
%F A338558 a(n) = 0 iff prime(n) is a term of A007659.
%t A338558 a[n_] := Module[{p = Prime[n]}, Min[Abs[Mod[RamanujanTau[p], {-p, p}]]]]; Array[a, 100] (* _Amiram Eldar_, Jan 10 2025 *)
%o A338558 (PARI) a(n) = my(p=prime(n)); abs(centerlift(Mod(ramanujantau(p), p)))
%Y A338558 Cf. A001220, A007540, A007659, A295645.
%Y A338558 A-values: A258367 (near-Wieferich), A250406 (near-Wilson), A244801 and A241014 (near-Wall-Sun-Sun), A260209 and A260210 (near-Wolstenholme).
%K A338558 nonn
%O A338558 1,6
%A A338558 _Felix Fröhlich_, Dec 21 2020