A064404 When the numerator - denominator (A064169) in n-th harmonic number is prime.

3, 4, 6, 7, 10, 19, 20, 26, 30, 31, 33, 40, 63, 85, 92, 100, 126, 131, 185, 196, 200, 204, 242, 246, 272, 274, 282, 379, 553, 572, 654, 777, 902, 1100, 1216, 1225, 1236, 1316, 1413, 1658, 1943, 2077, 2086, 2744, 2746, 2856, 2860, 3518, 3718, 4184, 4189, 4363

Offset: 1

Author

Robert G. Wilson v, Sep 28 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..92
• Henri Lifchitz and Renaud Lifchitz, PRP Records

Crossrefs

Cf. A064169.

Programs

Mathematica

s = 1; Do[ m = n; s = s + 1/n; If[ PrimeQ[ Numerator[ s ] - Denominator[ s ] ], Print[ n ] ], {n, 2, 2500} ]
hnoQ[n_]:=Module[{h=HarmonicNumber[n]},PrimeQ[Numerator[h]-Denominator[ h]]]; Select[Range[5000],hnoQ]  (* Harvey P. Dale, May 23 2012 *)

PARI

for(n=2, 300, if(isprime(lcm(n!, sum(k=2, n, 1/k))/n!), print1(n, ", "))); \\ Arkadiusz Wesolowski, Oct 13 2011

Extensions

More terms from Arkadiusz Wesolowski, Oct 13 2011