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A123538
Numbers n such that A064168(n) is prime.
1
1, 2, 3, 4, 5, 7, 9, 10, 11, 14, 15, 20, 27, 35, 36, 39, 48, 77, 96, 99, 102, 112, 131, 167, 176, 201, 212, 339, 356, 411, 490, 546, 656, 684, 839, 878, 904, 920, 981, 999, 1106, 1260, 1431, 1588, 2119, 2271, 2322, 2513, 2588, 2630, 3013, 3228, 3717, 3822, 3904, 4248, 6270, 6491, 7013, 7228, 7341, 7982, 8483, 9191, 9419, 10139, 10498, 12967, 13597, 13627, 13835, 15594
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, ...}.
Thus a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5 because A064168(n) is prime for n = {1, 2, 3, 4, 5}. The next term a(6) = 7 because A064168(7) = 503 is prime but A064168(6) = 69 is composite.
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