A121733 Numbers k such that tau(k) = tau(k+1) mod 691, where tau is Ramanujan's tau function A000594.

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

Cf. A000594, A046694, A121734.

Sequence in context: A234152 A234146 A164997 * A235250 A221931 A223117

Adjacent sequences: A121730 A121731 A121732 * A121734 A121735 A121736

Keyword

nonn

Author

Alexander Adamchuk, Aug 18 2006

Status

approved