A126839 Ramanujan numbers (A000594) read mod 11.

1, 9, 10, 2, 1, 2, 9, 0, 9, 9, 1, 9, 4, 4, 10, 7, 9, 4, 0, 2, 2, 9, 10, 0, 7, 3, 5, 7, 0, 2, 7, 8, 10, 4, 9, 7, 3, 0, 7, 0, 3, 7, 5, 2, 9, 2, 8, 4, 8, 8, 2, 8, 5, 1, 1, 0, 0, 0, 5, 9, 1, 8, 4, 3, 4, 2, 4, 7, 1, 4, 8, 0, 4, 5, 4, 0, 9, 8, 1, 7, 1, 5, 5, 4, 9, 1, 0, 0, 4, 4, 3, 9, 4, 6, 0, 3, 4, 6, 9, 3, 2, 7, 6

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

Crossrefs

Cf. A000594, this sequence (mod 11^1), A126840 (mod 11^2), A126841 (mod 11^3), A006571.

Programs

Mathematica

a[n_] := Mod[RamanujanTau[n], 11]; Array[a, 100] (* Amiram Eldar, Jan 05 2025 *)

PARI

a(n) = ramanujantau(n) % 11; \\ Amiram Eldar, Jan 05 2025

Formula

a(n) = A006571(n) (mod 11), n >= 1. For a proof see the Cowles link under A006571. See also the R. J. Mathar formula there. - Wolfdieter Lang, Feb 16 2016