A144248 -id:A144248 - cp's OEIS frontend

A128379 A000012^23 * A000594.

1, -1, -24, 0, 276, 300, -1748, -4300, 4278, 29026, 22724, -94668, -242398, -18722, 856980, 1472252, -384491, -5299269, -7824968, 2088032, 25655442, 38814478, -69160, -99735912, -175711283, -68736397, 294769680, 686373176, 562588924, -513324396, -2155273788, -2808874356

Offset: 1

Gary W. Adamson, Feb 28 2007

sign

Conjecture: given A000012^k * A000594, k=23 and 24 are the only k's generating sequences with zeros. k = 24 in A128378: (1, 0, -24, -24, 252, 552, -1196, -5496, ...).

Cf. A000594, A128378, A144248, A144249.

Nest[Accumulate, RamanujanTau[Range[32]], 23] (* Amiram Eldar, Jan 08 2025 *)

A000012 (partial sum operator) performed 23 times on A000594.

A144249 Apply partial sum operator twice to A000594.

Original entry on oeis.org

1, -22, 207, -1036, 2551, 90, -19115, 46160, -2208, -166496, 203828, 203208, -375150, -551652, 489006, 2516800, -2361340, -4512048, 3998664, 5399616, 2581080, -13068144, -10074096, 14208912, 12992695, 25642190, -34987395, -70969812, 21454401, 84666774, 95035979

Offset: 1

Vladimir Joseph Stephan Orlovsky, Sep 16 2008

sign

Cf. A000594.

Partial sums of A144248.

lst={};s1=0;s2=0;Do[s1=s1+RamanujanTau[n];s2=s2+s1;AppendTo[lst,s2],{n,5!}];lst
Nest[Accumulate, RamanujanTau[Range[32]], 2] (* Amiram Eldar, Jan 08 2025 *)

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

Original entry on oeis.org

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

Robert G. Wilson v, Dec 30 2002

nonn

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

Cf. A000594, A144248.

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 *)

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

Name corrected by Amiram Eldar, Jan 06 2025

cp's OEIS Frontend

A128379 A000012^23 * A000594.

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A144249 Apply partial sum operator twice to A000594.

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

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