A123538 Numbers n such that A064168(n) is prime.

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

Table of n, a(n) for n=1..72.

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

Cf. A064168, A118727, A001008, A002805, A056903, A067657.

Sequence in context: A122090 A066050 A004050 * A092999 A077154 A077273

Adjacent sequences: A123535 A123536 A123537 * A123539 A123540 A123541

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