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 A200980 Concatenate the digits of the natural numbers from 1 to n in order to build up two numbers x and y that minimize the ratio x/y > 0, an integer (leading zeros not admitted). 0
 1, 2, 4, 33, 5, 46, 6, 2, 2, 3, 2, 2, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n=8 and n=9 we have 12 possible different fractions: n=8 -> 3456/1728, 3528/1764, 3564/1782, 3654/1827, 4356/2178, 4716/2358, 5436/2718, 5634/2817, 7128/3564, 7164/3582, 8352/4176, 8712/4356. n=9 -> 13458/6729, 13584/6792, 13854/6927, 14538/7269, 14586/7293, 14658/7329, 15384/7692, 15846/7923, 15864/7932, 18534/9267, 18546/9273, 18654/9327. - Arie Groeneveld, Nov 25 2011 Examples for n=10..13: a(10) = 3 = 161427/53809, a(11) = 2 = 1141826/570913, a(12) = 2 = 11418226/5709113, and a(13) = 6 = 114312678/19052113. - Giovanni Resta, May 31 2016 LINKS Table of n, a(n) for n=1..13. EXAMPLE Starting with a(1)=1 we have a(2)=2/1=2, a(3)=12/3=4, a(4)=132/4=33, a(5)=215/43=5, a(6)= 2346/51= 46, a(7)= 3426/571=6, a(8)= 3456/1728 = 2, a(9)= 13458/6729=2. MAPLE with(combinat, permute); P:=proc(i) local a, c, d, j, k, m, ok, n, t, v, x, y; v:=[1, 2]; t:=2; lprint(1, 1); lprint(2, 2); for n from 3 to i do c:=n; for j from 1 to floor(1+evalf(log10(n))) do t:=t+1; v:=[op(v), c-10*trunc(c/10)]; c:=trunc(c/10); od; if (t mod 2)=1 then a:=(t+1)/2; else a:=t/2; fi; c:=permute(v); d:=nops(c); c:=op(c); m:=10^13; ok:=0; while ok=0 do for j from 1 to d do x:=0; for k from 1 to a do x:=10*x+c[j][k]; od; y:=0; for k from a+1 to t do y:=10*y+c[j][k]; od; if x>y then if trunc(x/y)=x/y then ok:=1; if x/y

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Last modified July 16 10:27 EDT 2024. Contains 374345 sequences. (Running on oeis4.)