A093408 For p = prime(n), the least k such that p is the numerator of a sum 1/k + 1/x1 +...+ 1/xm, where x1,...,xm (for any m) are distinct positive integers < k.

6, 2, 3, 4, 3, 4, 5, 4, 5, 5, 5, 6, 6, 8, 5, 7, 7, 5, 6, 7, 8, 8, 7, 7, 6, 8, 7, 5, 8, 8, 6, 7, 5, 8, 8, 10, 8, 9, 9, 7, 8, 10, 9, 9, 10, 8, 7, 7, 8, 8, 10, 8, 8, 9, 10, 9, 8, 8, 9, 9, 8, 7, 9, 8, 10, 7, 10, 9, 10, 10, 8, 9, 8, 10, 9, 10, 7, 9, 9, 11, 10, 9, 9, 10, 10, 9, 10, 7, 9, 9, 11, 10, 9, 14, 14

Offset

1,1

Links

Table of n, a(n) for n=1..95.

Eric Weisstein's World of Mathematics, Egyptian Fraction

Example

a(1) = 6 because 2 = prime(1) and 1/2 + 1/6 = 2/3, whose numerator is 2.

Mathematica

len=100; a=Table[0, {len}]; done=False; s={0}; n=0; While[ !done, n++; s=Join[s, s+1/n]; ns=Numerator[s]; done=True; Do[If[a[[i]]==0, p=Prime[i]; If[Count[ns, p]>0, a[[i]]=n, done=False]], {i, len}]]; a

Crossrefs

Cf. A093407.

Sequence in context: A307234 A371875 A021620 * A222223 A284821 A145680

Adjacent sequences: A093405 A093406 A093407 * A093409 A093410 A093411

Keyword

nonn

Author

T. D. Noe, Mar 29 2004

Status

approved