A136683 Numbers k such that A136675(k) is prime.

2, 3, 4, 5, 6, 9, 20, 21, 29, 119, 132, 151, 351, 434, 457, 462, 572, 611, 930, 1107, 1157, 1452, 1515, 2838, 3997, 5346, 6463, 6725, 7664, 10234, 14168, 14299

Offset: 1

Author

Alexander Adamchuk, Jan 16 2008

Keywords

• nonn
• more

Comments

A136675(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j^3.

Links

• Eric Weisstein's World of Mathematics, Harmonic Number

Crossrefs

Cf. A058313, A119682, A120296, A136675, A136676, A136677.

Cf. A001008, A007406, A007408, A007410, A099828, A103345.

Cf. A136681, A136682, A136684, A136685, A136686.

Programs

Mathematica

Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k^3, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,151} ]
Flatten[Position[Numerator[Accumulate[Table[(-1)^(k+1) 1/k^3,{k,3000}]]],?PrimeQ] ] (* _Harvey P. Dale, Feb 12 2013 *)

PARI

isok(n) = ispseudoprime(numerator(sum(k=1, n, (-1)^(k+1) / k^3))); \\ Daniel Suteu, Mar 15 2019

Extensions

More terms from Harvey P. Dale, Feb 12 2013

a(25)-a(28) from Amiram Eldar, Mar 15 2019

a(29)-a(32) from Robert Price, Apr 22 2019