A121742 Numbers k such that three consecutive Ramanujan tau numbers are congruent mod 691, or A000594(k) == A000594(k+1) == A000594(k+2) mod 691, or A046694(k) = A046694(k+1) = A046694(k+2).

290217, 477155, 1051085, 1153412, 1409635, 1409636, 1641812, 2056412, 2657865, 2945116, 3724928, 4570784, 5115359, 5187777, 5567783, 5720418, 7836078, 8736807, 8932428, 9618716, 9957630, 10175867, 10447914, 10547421, 10982172, 11359120, 11499876, 11735611, 12651355, 13018169, 13515452, 13867914

Offset: 1

Author

Alexander Adamchuk, Aug 19 2006

Keywords

• nonn

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 triples 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

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

Crossrefs

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

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}]

Extensions

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

More terms from Jud McCranie, Nov 02 2020