|
%I #15 Jan 26 2020 11:03:54
%S 184,2103,3421,3638,4342,5181,6029,6233,8323,8628,8721,9658,9905,
%T 11322,11774,11888,12410,12774,12811,13063,13484,14744,14906,15065,
%U 15247,16581,16610,18248,18396,18703,19514,20476,20479,21657,22089,22984
%N Numbers k such that tau(k) = tau(k+1) mod 691, where tau is Ramanujan's tau function A000594.
%C 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TauFunction.html">Ramanujan's Tau Function</a>.
%e a(1) = 184 because the first pair of equal consecutive numbers in A046694 is A046694(184) = A046694(185) = 483 = A121734(1).
%t Select[Range[30000],Mod[DivisorSigma[11,#1],691]==Mod[DivisorSigma[11,#1+1],691]&]
%o (PARI) is(n)=(ramanujantau(n)-ramanujantau(n+1))%691==0 \\ _Charles R Greathouse IV_, Feb 08 2017
%Y Cf. A000594, A046694, A121734.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Aug 18 2006
|
