1,2

Ramanujan tau is multiplicative, so this sequence is multiplicative mod 691.

There are pairs of identical terms a(n) and a(n+1). The first such twin pair is a(184) = a(185) = 483. The indices for a first twin in a pair are listed in A121733. Corresponding twin values are listed in A121734. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 18 2006

Set of values of a(n) consists of all integers from 0 to 690. The first a(n) = 0 occur at n = 2*691 - 1 = 1381 that is a prime. Set of numbers n such that a(n) = 0 is a union of all terms of the arithmetic progressions k*p, where p is a prime of the form p = 2m*691 - 1, and k>0 is an integer. Primes of the form p = 2m*691 - 1 are listed in A134671 = {1381,5527,8291,12437,22111,29021,30403,...}. It appears that in a(n) there are strings of consecutive zeros of any length. The first pair of consecutive zeros occurs at n = {16581,16582}. The least numbers k such that a(n) has a string of n consecutive zeros starting with a(k) are listed in A134670(n) = {1381,16581,290217,1409635,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 05 2007

H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

T. D. Noe, Table of n, a(n) for n=1..10000

Coefficient of x^2 in tau(x) = -24; 1^11+2^11 = 2049 = 667 mod 691 = -24 mod 691.

Cf. A000594, A013959, A121733, A121734, A126811-...

Cf. A134670, A134671, A121742, A121743.

Sequence in context: A051003 A104181 A057564 this_sequence A138563 A092797 A105212

Adjacent sequences: A046691 A046692 A046693 this_sequence A046695 A046696 A046697

easy,nice,nonn

Marc LeBrun (mlb(AT)well.com)