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

0, 276, 91, 79, 0, 0, 0, 0, 76, 349, 212, 355, 662, 227, 342, 616, 182, 641, 105, 0, 21, 33, 0, 0, 316, 436, 346, 109, 468, 557, 261, 512, 299, 532, 565, 214, 72, 218, 436, 0, 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

Offset: 1

Author

Alexander Adamchuk, Aug 19 2006

Keywords

• nonn

Comments

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.

Links

• Jud McCranie, Table of n, a(n) for n = 1..2568
• Eric Weisstein Ramanujan's Tau Function.

Crossrefs

Cf. A000594, A046694, A121733, A121734, A121742.

Programs

Mathematica

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}]
Select[Partition[Table[Mod[DivisorSigma[11,n],691],{n,10000000}],3,1],Length[ Union[#]]==1&][[All,1]] (* Harvey P. Dale, Jan 31 2020 *)

Formula

a(n) = A000594(A121742(n)) mod 691.

a(n) = A046694(A121742(n)).

Extensions

a(7)-a(16) from Amiram Eldar, Jan 26 2020

More terms by Jud McCranie Nov 02 2020