OFFSET
1,2
COMMENTS
A001008(n) + A002805(n) = A064168(n) is the sum of numerator and denominator in n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n = A001008(n)/A002805(n). Corresponding primes in A064168(n) are listed in A118727(n) = A064168[a(n)] = {2, 5, 17, 37, 197, 503, 9649, 9901, 111431, ...} Primes that are the sum of the numerator and denominator of a harmonic number.
LINKS
Eric Weisstein, The World of Mathematics: Harmonic Number.
EXAMPLE
Harmonic numbers begin H(n) = [ 1/1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520,... ].
A064168(n) begins {2, 5, 17, 37, 197, 69, 503, 1041, 9649, 9901, ...}.
MAPLE
N:= 10^4: # to get terms <= N
H:= ListTools:-PartialSums([seq(1/i, i=1..N)]):
select(t -> isprime(numer(H[t])+denom(H[t])), [$1..N]); # Robert Israel, May 30 2019
MATHEMATICA
s=0; Do[s=s+1/n; ss=Numerator[s]+Denominator[s]; If[PrimeQ[ss], Print[{n, ss}]], {n, 1, 1106}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Nov 11 2006
EXTENSIONS
More terms from Stefan Steinerberger, May 13 2007
More terms from Robert Israel, May 30 2019
STATUS
approved