

A076474


Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator.


2



1, 2, 3, 5, 6, 10, 11, 13, 21, 23, 24, 29, 45, 48, 50, 51, 53, 54, 57, 58, 60, 68, 70, 81, 82, 98, 103, 104, 106, 120, 125, 128, 132, 139, 149, 164, 170, 192, 206, 214, 226, 228, 232, 235, 241, 257, 270, 275, 283, 305, 307, 314, 326, 351, 399, 412, 423, 436, 520
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OFFSET

1,2


COMMENTS

By Dirichlet's Theorem, it is always possible to find the next term. See A076475 for the list of primes appearing in the numerator. Does this sum of unit fractions converge?


LINKS

Table of n, a(n) for n=1..59.


EXAMPLE

For example, 1/1 + 1/2 = 3/2, 1/1 + 1/2 + 1/3 = 11/6. However, 1/4 is not in the sequence because 1/1 + 1/2 + 1/3 + 1/4 = 25/12 and 25 is not prime.


MATHEMATICA

nMax = 100; lst = {1}; numer = {1}; s = 1; i = 2; Do[While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[lst, i]; AppendTo[numer, Numerator[s]]; i++, {n, 2, nMax}]; lst


CROSSREFS

Cf. A076475.
Cf. A127515, A134411.
Sequence in context: A316503 A316494 A178992 * A255059 A057760 A074243
Adjacent sequences: A076471 A076472 A076473 * A076475 A076476 A076477


KEYWORD

nonn,frac


AUTHOR

T. D. Noe, Oct 14 2002


STATUS

approved



