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A121743 Values of the Ramanujan tau triples mod 691 such that three consecutive Ramanujan tau numbers are congruent mod 691.

%I A121743 #23 Feb 16 2025 08:33:02
%S A121743 0,276,91,79,0,0,0,0,76,349,212,355,662,227,342,616,182,641,105,0,21,
%T A121743 33,0,0,316,436,346,109,468,557,261,512,299,532,565,214,72,218,436,0,
%U A121743 166,532,0,591,0,144,0,544,257,0,0,0,422,0,0,488,0,0,0,488,0,233,371,0,380,28,0,641,414,331,0,487,0,666,130,14,0,0,321,620,0,339,533
%N A121743 Values of the Ramanujan tau triples mod 691 such that three consecutive Ramanujan tau numbers are congruent mod 691.
%C A121743 Corresponding indices of the Ramanujan tau triples mod 691 are listed in A121742. All a(n) belong to the Ramanujan tau twins mod 691 A121734(n). There are also quadruplets in the Ramanujan tau mod 691 such that A046694(n) = A046694(n+1) = A046694(n+2) = A046694(n+3). The first such Ramanujan tau quadruplet mod 691 starts with A046694(1409635) = 0.
%H A121743 Jud McCranie, <a href="/A121743/b121743.txt">Table of n, a(n) for n = 1..2568</a>
%H A121743 Eric Weisstein <a href="https://mathworld.wolfram.com/TauFunction.html">Ramanujan's Tau Function</a>.
%F A121743 a(n) = A000594(A121742(n)) mod 691.
%F A121743 a(n) = A046694(A121742(n)).
%t A121743 Do[f=Mod[DivisorSigma[11,n],691];g=Mod[DivisorSigma[11,n+1],691];h=Mod[DivisorSigma[11,n+2],691];If[f==g&&g==h,Print[{n,f}]],{n,1,1500000}]
%t A121743 Select[Partition[Table[Mod[DivisorSigma[11,n],691],{n,10000000}],3,1],Length[ Union[#]]==1&][[All,1]] (* _Harvey P. Dale_, Jan 31 2020 *)
%Y A121743 Cf. A000594, A046694, A121733, A121734, A121742.
%K A121743 nonn
%O A121743 1,2
%A A121743 _Alexander Adamchuk_, Aug 19 2006
%E A121743 a(7)-a(16) from _Amiram Eldar_, Jan 26 2020
%E A121743 More terms by _Jud McCranie_ Nov 02 2020