A076474 Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator.

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

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 * A324968 A255059 A057760

Adjacent sequences: A076471 A076472 A076473 * A076475 A076476 A076477

Keyword

nonn,frac

Author

T. D. Noe, Oct 14 2002

Status

approved