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 A121733 #16 Feb 16 2025 08:33:02 %S A121733 184,2103,3421,3638,4342,5181,6029,6233,8323,8628,8721,9658,9905, %T A121733 11322,11774,11888,12410,12774,12811,13063,13484,14744,14906,15065, %U A121733 15247,16581,16610,18248,18396,18703,19514,20476,20479,21657,22089,22984 %N A121733 Numbers k such that tau(k) = tau(k+1) mod 691, where tau is Ramanujan's tau function A000594. %C A121733 Corresponding Ramanujan tau numbers mod 691 are listed in A121734(n) = A046694(a(n)). A121734 begins 483, 209, 21, 632, 650, 541, 546, 281, 666, 440, 397, 576, 18, 251, 356, 207, 532, 361, 121, 642, 288, 167, 348, 505, 561, 0, 108, 166, 97, 492, 58, 255, 632, 151, 679, 185, 141, 587, 0, .... %C A121733 There are instances of three consecutive equal terms in A046694, with A046694(n) = A046694(n+1) = A046694(n+2). Equivalently there are consecutive equal terms a(n) = a(n+1). The first is A046694(290217) = A046694(290218) = A046694(290219) = 0. - _Alexander Adamchuk_, Aug 18 2006 %H A121733 Amiram Eldar, <a href="/A121733/b121733.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2500 from Charles R Greathouse IV) %H A121733 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TauFunction.html">Ramanujan's Tau Function</a>. %e A121733 a(1) = 184 because the first pair of equal consecutive numbers in A046694 is A046694(184) = A046694(185) = 483 = A121734(1). %t A121733 Select[Range[30000],Mod[DivisorSigma[11,#1],691]==Mod[DivisorSigma[11,#1+1],691]&] %o A121733 (PARI) is(n)=(ramanujantau(n)-ramanujantau(n+1))%691==0 \\ _Charles R Greathouse IV_, Feb 08 2017 %Y A121733 Cf. A000594, A046694, A121734. %K A121733 nonn %O A121733 1,1 %A A121733 _Alexander Adamchuk_, Aug 18 2006