

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.


4



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
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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: A082503 A190549 A064442 * A126044 A114899 A220906
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



