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A118727 Primes that are the sum of the numerator and denominator of a harmonic number. 1
2, 5, 17, 37, 197, 503, 9649, 9901, 111431, 1532093, 1556117, 71354639, 392849685203, 67564865715709, 67929521152309, 2551756396706233, 345246028268898566519, 73744425850091533377950933665103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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..}.

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

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

a(1) = 1 + 1 = 2,

a(2) = 3 + 2 = 5,

a(3) = 11 + 6 = 17,

a(4) = 25 + 12 = 37,

a(5) = 137 + 60 = 197,

a(6) = 363 + 140 = 503,

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

MATHEMATICA

Select[Numerator[#]+Denominator[#]&/@HarmonicNumber[Range[100]], PrimeQ] (* Harvey P. Dale, Jan 29 2014 *)

CROSSREFS

Cf. A064168, A001008, A002805.

Sequence in context: A002496 A127436 A064168 * A183906 A042361 A114300

Adjacent sequences:  A118724 A118725 A118726 * A118728 A118729 A118730

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, May 21 2006

STATUS

approved

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