A295645 Primes p such that tau(p) +- 1 is congruent to 0 (mod p), where tau is the Ramanujan tau function (A000594).

11, 23, 691, 5807

Offset

1,1

Comments

Nik Lygeros and Olivier Rozier found a new solution to the equation tau(p) + 1 == 0 (mod p) for prime p = 692881373, on September 6 2009. - Seiichi Manyama, Dec 30 2017

a(5) > 8*10^7. - Seiichi Manyama, Jan 01 2018

A superset of A193855. - Jud McCranie, Nov 06 2020

Links

Table of n, a(n) for n=1..4.

N. Lygeros and O. Rozier, A new solution to the equation tau(p) == 0 (mod p), J. Int. Seq. 13 (2010) # 10.7.4.

Eric Weisstein's World of Mathematics, Tau Function.

Wikipedia, Ramanujan tau function.

Example

tau(11) = 534612 and 11 | (534612 - 1), so a(1) = 11.
tau(23) = 18643272 and 23 | (18643272 - 1), so a(2) = 23.
tau(691) = -2747313442193908 and 691 | (-2747313442193908 - 1), so a(3) = 691.
tau(5807) = 237456233554906855056 and 5807 | (237456233554906855056 + 1), so a(4) = 5807.

Mathematica

Select[Prime@ Range[10^3], Function[p, AnyTrue[RamanujanTau[p] + {-1, 1}, Divisible[#, p] &]]] (* Michael De Vlieger, Dec 30 2017 *)

Prog

(PARI) isok(p) = my(rp=ramanujantau(p)); isprime(p) && !((rp-1) % p) || !((rp+1) % p); \\ Michel Marcus, Nov 07 2020

Crossrefs

Cf. A000594, A076847 (tau(p)), A007659, A193855, A273650, A295654.

Sequence in context: A005485 A041240 A193855 * A295654 A247347 A045498

Adjacent sequences: A295642 A295643 A295644 * A295646 A295647 A295648

Keyword

nonn,more

Author

Seiichi Manyama, Nov 25 2017

Status

approved