A076724 Numbers m such that abs(Sum {k = 1..m} tau(k)) is a prime, where tau is the Ramanujan tau function (A000594).

2, 3, 39, 97, 172, 177, 200, 203, 318, 332, 345, 500, 519, 527, 651, 660, 722, 865, 870, 881, 890, 897, 1089, 1091, 1101, 1106, 1156, 1177, 1192, 1205, 1369, 1370, 1393, 1425, 1459, 1466, 1499, 1500, 1503, 1505, 1517, 1519, 1703, 1755, 1779, 1782, 1786

Offset: 1

Author

Robert G. Wilson v, Dec 30 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000594, A144248.

Programs

Mathematica

s = 0; Do[s = s + RamanujanTau[n]; If[PrimeQ[s], Print[n]], {n, 1, 10^4}]
Flatten[Position[Accumulate[RamanujanTau[Range[0,1800]]],?(PrimeQ[ #]&)]]-1 (* _Harvey P. Dale, Dec 22 2015 *)

PARI

list(lim) = {my(s = 0); for(k = 1, lim, s += ramanujantau(k); if(isprime(abs(s)), print1(k, ", ")));} \\ Amiram Eldar, Jan 06 2025

Extensions

Name corrected by Amiram Eldar, Jan 06 2025