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

Author

Alexander Adamchuk, Aug 18 2006

Keywords

• nonn

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

Examples

			a(1) = 184 because the first pair of equal consecutive numbers in A046694 is A046694(184) = A046694(185) = 483 = A121734(1).
		

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.

Crossrefs

Cf. A000594, A046694, A121734.

Programs

Mathematica

Select[Range[30000],Mod[DivisorSigma[11,#1],691]==Mod[DivisorSigma[11,#1+1],691]&]

PARI

is(n)=(ramanujantau(n)-ramanujantau(n+1))%691==0 \\ Charles R Greathouse IV, Feb 08 2017