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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.

%I A154429 #13 Oct 04 2023 15:30:58
%S A154429 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,
%T A154429 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,
%U A154429 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
%N 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.
%D A154429 J. Steuding, Diophantine Analysis, Chapman & Hall/CRC, 2005, pp. 39-40, 50.
%H A154429 Seiichi Manyama, <a href="/A154429/b154429.txt">Table of n, a(n) for n = 1..10000</a>
%H A154429 D. Eppstein, <a href="http://www.ics.uci.edu/~eppstein/numth/egypt/">Egyptian fractions</a>
%e A154429 For n=3, the Greedy Algorithm gives 8/73=1/10+1/105+1/15330
%t A154429 GreedyPart[q_Integer] := 0;
%t A154429 GreedyPart[Rational[1, y_]] := 0;
%t A154429 GreedyPart[q_Rational] := q - If[q < 0 || q > 1, Floor[q], Rational[1, 1 + Quotient[1, q]]];
%t A154429 SubtractShifted[l_] := Drop[l, -2] - Take[l, {2, -2}];
%t A154429 EgyptGreedy[q_] := SubtractShifted[FixedPointList[GreedyPart, q]];
%t A154429 terms := 200;
%t A154429 For[i = 25, i <= 24*terms + 1, i = i + 24,k = 2;While[Length[EgyptGreedy[4k/i]]> 3, k++ ];Print[k]]
%K A154429 nonn
%O A154429 1,1
%A A154429 Matthew McMullen (mmcmullen(AT)otterbein.edu), Jan 09 2009
%E A154429 More terms from _Seiichi Manyama_, Sep 21 2022