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A121742 Numbers n such that three consecutive Ramanujan tau numbers are congruent mod 691, or A000594[n] == A000594[n+1] == A000594[n+2] mod 691, or A046694[n] = A046694[n+1] = A046694[n+2]. 4
290217, 477155, 1051085, 1153412, 1409635, 1409636 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

Corresponding Ramanujan tau numbers mod 691 are listed in A121743[n] = A046694[a(n)]. A121743[n] begins {0,276,91,79,0,0,...}. a(n) are the indices of the first number in the Ramanujan tau triplets mod 691. All a(n) belong to A121733[n] - indices of the first number in the Ramanujan tau twins mod 691. 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

Eric Weisstein Link to a section of The World of Mathematics. Ramanujan's Tau Function.

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}]

CROSSREFS

Cf. A121743, A121733, A121734, A046694, A000594.

Sequence in context: A096519 A157112 A043616 * A093792 A068241 A168500

Adjacent sequences:  A121739 A121740 A121741 * A121743 A121744 A121745

KEYWORD

nonn

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 19 2006

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Last modified February 14 19:37 EST 2012. Contains 205663 sequences.