A134411 a(n) is the smallest positive integer such that the numerator of (Sum_{k=1..n} 1/a(k)) is prime (or 1), for all positive integers n.

1, 1, 1, 2, 3, 1, 3, 1, 1, 2, 6, 1, 1, 2, 4, 1, 1, 1, 3, 1, 1, 2, 3, 1, 2, 3, 2, 1, 4, 6, 1, 3, 1, 3, 2, 8, 3, 2, 3, 3, 1, 2, 6, 2, 1, 3, 3, 1, 5, 4, 3, 2, 1, 3, 1, 4, 2, 1, 3, 2, 1, 3, 1, 1, 3, 1, 1, 2, 6, 2, 4, 5, 3, 1, 3, 2, 1, 3, 3, 1, 3

Offset

1,4

Links

Table of n, a(n) for n=1..81.

Example

The sum of the reciprocals of the first 9 terms is 1 + 1 + 1 + 1/2 + 1/3 + 1 + 1/3 + 1 + 1 = 43/6. (And the numerator, 43, is prime.) Adding the reciprocal of 1 to this gets 49/6 (in reduced form). But 49 is composite. However, adding the reciprocal of 2 to 43/6 gets 23/3 (when written in reduced form). 23 is a prime, so therefore a(10) = 2.

Mathematica

a = {1}; s = 1; Do[i = 1; While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[a, i], {80}]; a (* Stefan Steinerberger, Oct 27 2007 *)

Crossrefs

Cf. A134412, A134413.

Sequence in context: A353640 A064442 A287566 * A126044 A342344 A342101

Adjacent sequences: A134408 A134409 A134410 * A134412 A134413 A134414

Keyword

nonn

Author

Leroy Quet, Oct 24 2007

Extensions

More terms from Stefan Steinerberger, Oct 27 2007

Status

approved