A125504 Smallest number k such that the numerator of alternating generalized harmonic number H'(k,n) = Sum[ (-1)^(i+1) * 1/i^n, {i,1,k} ] is a prime.

3, 2, 2, 3, 2, 19, 2, 146, 87, 3, 16, 3, 2, 249, 15, 87, 2, 699, 2

Offset: 1

Author

Alexander Adamchuk, Dec 28 2006, Jan 31 2007

Keywords

• hard
• more
• nonn

Comments

a(n) = 2 for n in A000043.

a(n) = 3 for n in {1,4,10,12,24,27,39,...}.

a(n) = 5 for n in {26,76,132,205,238,...}.

a(n) = 9 for n in {100,200,...}.

a(n) = 15 for n in {15,33,65,...}.

a(21) = 18. a(22) = 13. a(41) = 6. a(72) = 11. a(173) = 8.

a(20) > 2100 - Max Alekseyev, Jul 07 2009

Links

• Eric Weisstein's World of Mathematics, Harmonic Number

Crossrefs

Cf. A058313, A119682, A120296, A001008, A000043.

Extensions

More terms from Max Alekseyev, Jul 07 2009