A154429 a(n) is the least k such that the greedy algorithm (for Egyptian fractions) on 4k/(24n+1) terminates in at most three steps.

2, 2, 2, 5, 3, 4, 13, 2, 2, 7, 5, 51, 4, 4, 5, 2, 3, 5, 5, 7, 5, 6, 2, 5, 11, 4, 3, 5, 5, 2, 2, 7, 4, 5, 29, 2, 2, 2, 5, 8, 4, 11, 2, 2, 6, 4, 11, 5, 3, 11, 2, 5, 5, 5, 7, 4, 37, 2, 3, 3, 4, 7, 5, 5, 2, 2, 17, 5, 5, 54, 2, 2, 2, 5, 7, 4, 11, 2, 2, 6, 5, 3, 4, 5, 10, 2, 7, 5, 5, 7, 5, 12, 2, 3, 10, 4, 7, 5, 5, 2

Offset

1,1

References

J. Steuding, Diophantine Analysis, Chapman & Hall/CRC, 2005, pp. 39-40, 50.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

D. Eppstein, Egyptian fractions

Example

For n=3, the Greedy Algorithm gives 8/73=1/10+1/105+1/15330

Mathematica

GreedyPart[q_Integer] := 0;
GreedyPart[Rational[1, y_]] := 0;
GreedyPart[q_Rational] := q - If[q < 0 || q > 1, Floor[q], Rational[1, 1 + Quotient[1, q]]];
SubtractShifted[l_] := Drop[l, -2] - Take[l, {2, -2}];
EgyptGreedy[q_] := SubtractShifted[FixedPointList[GreedyPart, q]];
terms := 200;
For[i = 25, i <= 24*terms + 1, i = i + 24, k = 2; While[Length[EgyptGreedy[4k/i]]> 3, k++ ]; Print[k]]

Crossrefs

Sequence in context: A174960 A210239 A115253 * A333388 A174577 A194684

Adjacent sequences: A154426 A154427 A154428 * A154430 A154431 A154432

Keyword

nonn

Author

Matthew McMullen (mmcmullen(AT)otterbein.edu), Jan 09 2009

Extensions

More terms from Seiichi Manyama, Sep 21 2022

Status

approved