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

2, 5, 17, 37, 197, 503, 9649, 9901, 111431, 1532093, 1556117, 71354639, 392849685203, 67564865715709, 67929521152309, 2551756396706233, 345246028268898566519, 73744425850091533377950933665103, 4418089000986947559043789457061782529431

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..} = A123538.

Links

Robert Israel, Table of n, a(n) for n = 1..46

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...

Maple

select(isprime, map(numer+denom, ListTools:-PartialSums([(1/n) $ n=1..10^3]))); # Robert Israel, May 30 2019

Mathematica

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

Crossrefs

Cf. A064168, A001008, A002805, A123538.

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