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A076474
Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator (or 1 in the first sum).
3
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?
EXAMPLE
2 is a term because 1/1 + 1/2 = 3/2 and 3 is prime.
3 is a term because 1/1 + 1/2 + 1/3 = 11/6 and 11 is prime.
4 is not in a term 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
KEYWORD
nonn,frac,changed
AUTHOR
T. D. Noe, Oct 14 2002
STATUS
approved