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A118727 Primes that are the sum of the numerator and denominator of a harmonic number. 1

%I

%S 2,5,17,37,197,503,9649,9901,111431,1532093,1556117,71354639,

%T 392849685203,67564865715709,67929521152309,2551756396706233,

%U 345246028268898566519,73744425850091533377950933665103

%N Primes that are the sum of the numerator and denominator of a harmonic number.

%C A001008(n) + A002805(n) = A064168(n) is the sum of numerator and denominator in n-th harmonic number H(n) = 1 + 1/2 + 1/3 +...+ 1/n. A064168(n) is prime for n = {1,2,3,4,5,7,9,10,11,14,15,20,27,35,36,39,48..}.

%e H(n) = [ 1/1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520,... ].

%e a(1) = 1 + 1 = 2,

%e a(2) = 3 + 2 = 5,

%e a(3) = 11 + 6 = 17,

%e a(4) = 25 + 12 = 37,

%e a(5) = 137 + 60 = 197,

%e a(6) = 363 + 140 = 503,

%e a(7) = 7129 + 2520 = 9649...

%t Select[Numerator[#]+Denominator[#]&/@HarmonicNumber[Range[100]],PrimeQ] (* _Harvey P. Dale_, Jan 29 2014 *)

%Y Cf. A064168, A001008, A002805.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, May 21 2006

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Last modified January 19 22:02 EST 2018. Contains 297938 sequences.