A126845 Ramanujan numbers (A000594) read mod 23.

1, 22, 22, 0, 0, 1, 0, 1, 0, 0, 0, 0, 22, 0, 0, 22, 0, 0, 0, 0, 0, 0, 1, 22, 1, 1, 1, 0, 22, 0, 22, 0, 0, 0, 0, 0, 0, 0, 1, 0, 22, 0, 0, 0, 0, 22, 22, 1, 1, 22, 0, 0, 0, 22, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 22, 0, 22, 0, 22, 0, 22, 0, 0, 22, 0, 0, 22, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane, Feb 25 2007

Keywords

• nonn

References

• G. H. Hardy, Ramanujan, Twelve Lectures on Subjects Suggested by His Life and Work, Cambridge, 1940, p. 166.

Links

• Amiram Eldar, 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, A011586.

Programs

Mathematica

a[n_] := Mod[RamanujanTau[n], 23]; Array[a, 100] (* Amiram Eldar, Jan 04 2025 *)

PARI

a(n) = ramanujantau(n) % 23; \\ Amiram Eldar, Jan 04 2025

Formula

a(n) = 0 if Legendre symbol (n,23) = A011586(n) = -1 (Hardy, 1940). - Amiram Eldar, Jan 04 2025