cp's OEIS Frontend

A074078 Number of steps to reach an integer starting with s = n/3 and iterating the map x -> s*ceiling(x).

%I A074078 #12 Jan 09 2025 18:54:25
%S A074078 0,2,4,0,1,1,0,13,2,0,3,2,0,1,1,0,2,4,0,8,5,0,1,1,0,7,9,0,2,7,0,1,1,0,
%T A074078 3,2,0,6,2,0,1,1,0,2,3,0,10,3,0,1,1,0,3,3,0,2,3,0,1,1,0,5,2,0,5,2,0,1,
%U A074078 1,0,2,10,0,3,7,0,1,1,0,8,4,0,2,6,0,1,1,0,5,2,0,3,2,0,1,1,0,2,5,0,4,6,0,1,1,0
%N A074078 Number of steps to reach an integer starting with s = n/3 and iterating the map x -> s*ceiling(x).
%H A074078 Michael S. Branicky, <a href="/A074078/b074078.txt">Table of n, a(n) for n = 3..10002</a>
%e A074078 s = 5/3 -> 10/3 -> 20/3 -> 35/3 -> 20, so a(5) = 4.
%p A074078 f := proc(b1,b2) local c1,c2,t1,t2,t3,t4,i; c1 := numer(b1/b2); c2 := denom(b1/b2); i := 0; while c2 <> 1 do i := i+1; t1 := ceil(c1/c2); t2 := b1*t1; t3 := t2/b2; c1 := numer(t3); c2 := denom(t3); od: RETURN(i); end; [seq(f(n,3),n=4..120)];
%t A074078 ce[n_] := Length[NestWhileList[(n/3)*Ceiling[#] &, n/3, ! IntegerQ[#] &]] - 1; Table[ce[n], {n, 3, 108}] (* _Jayanta Basu_, Jul 30 2013 *)
%o A074078 (Python)
%o A074078 from math import ceil
%o A074078 from fractions import Fraction
%o A074078 def a(n):
%o A074078     s = Fraction(n, 3)
%o A074078     x, c = s, 0
%o A074078     while x.denominator != 1:
%o A074078         U = ceil(x)
%o A074078         x, c = U*s, c+1
%o A074078     return c
%o A074078 print([a(n) for n in range(3, 109)]) # _Michael S. Branicky_, Jan 09 2025
%Y A074078 Cf. A072340, A074090, A074091, A074096. Records are in A074097, A074098.
%Y A074078 First integer reached: A081852.
%K A074078 nonn
%O A074078 3,2
%A A074078 _N. J. A. Sloane_, Sep 16 2002