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A121743
Values of the Ramanujan tau triples mod 691 such that three consecutive Ramanujan tau numbers are congruent mod 691.
7
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
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
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