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

1,2

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.

Formula

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

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

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 *)

Crossrefs

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

Sequence in context: A133536 A224109 A075666 * A084802 A309998 A003903

Adjacent sequences: A121740 A121741 A121742 * A121744 A121745 A121746

Keyword

nonn

Author

Alexander Adamchuk, Aug 19 2006

Extensions

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

More terms by Jud McCranie Nov 02 2020

Status

approved