Search: id:A046694
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%I A046694
%S A046694 1,667,252,601,684,171,531,178,372,168,469,123,629,385,309,388,611,55,
               672,
%T A046694 630,449,491,92,632,57,106,88,580,173,185,366,666,27,538,429,379,622,456,
%U A046694 269,136,87,280,36,632,160,556,435,345,194,14,570,52,209,652,172,542,49
%N A046694 Ramanujan tau numbers mod 691 = sum of 11-th power of divisors mod 691.
%C A046694 Ramanujan tau is multiplicative, so this sequence is multiplicative mod 
               691.
%C A046694 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
%C A046694 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
%D A046694 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.
%H A046694 T. D. Noe, <a href="b046694.txt">Table of n, a(n) for n=1..10000</a>
%e A046694 Coefficient of x^2 in tau(x) = -24; 1^11+2^11 = 2049 = 667 mod 691 = 
               -24 mod 691.
%Y A046694 Cf. A000594, A013959, A121733, A121734, A126811-...
%Y A046694 Cf. A134670, A134671, A121742, A121743.
%Y A046694 Sequence in context: A051003 A104181 A057564 this_sequence A138563 A092797 
               A105212
%Y A046694 Adjacent sequences: A046691 A046692 A046693 this_sequence A046695 A046696 
               A046697
%K A046694 easy,nice,nonn
%O A046694 1,2
%A A046694 Marc LeBrun (mlb(AT)well.com)

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