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A121733
Numbers k such that tau(k) = tau(k+1) mod 691, where tau is Ramanujan's tau function A000594.
9
184, 2103, 3421, 3638, 4342, 5181, 6029, 6233, 8323, 8628, 8721, 9658, 9905, 11322, 11774, 11888, 12410, 12774, 12811, 13063, 13484, 14744, 14906, 15065, 15247, 16581, 16610, 18248, 18396, 18703, 19514, 20476, 20479, 21657, 22089, 22984
OFFSET
1,1
COMMENTS
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, ....
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Charles R Greathouse IV)
Eric Weisstein's World of Mathematics, Ramanujan's Tau Function.
EXAMPLE
a(1) = 184 because the first pair of equal consecutive numbers in A046694 is A046694(184) = A046694(185) = 483 = A121734(1).
MATHEMATICA
Select[Range[30000], Mod[DivisorSigma[11, #1], 691]==Mod[DivisorSigma[11, #1+1], 691]&]
PROG
(PARI) is(n)=(ramanujantau(n)-ramanujantau(n+1))%691==0 \\ Charles R Greathouse IV, Feb 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Aug 18 2006
STATUS
approved