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 A372010 a(n) is the n-digit number k such that R(k)/k is maximal for any n-digit number. 1
 1, 19, 109, 1099, 10099, 100999, 1000999, 10009999, 100009999, 1000099999, 10000099999, 100000999999, 1000000999999, 10000009999999, 100000009999999, 1000000099999999, 10000000099999999, 100000000999999999, 1000000000999999999, 10000000009999999999, 100000000009999999999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..21. Michael S. Branicky, Proof of form of a(n) for OEIS A372010 Index entries for linear recurrences with constant coefficients, signature (11,0,-110,100). FORMULA a(n) = 1 0^(n-1-h) 9^h, where h = floor(n/2) and ^ represents repeated concatenation (see links for proof). a(n) = 10^(n-1) + 10 ^ floor(n / 2) - 1. G.f.: x*(1 + 8*x - 100*x^2 + 10*x^3)/((1 - x)*(1 - 10*x)*(1 - 10*x^2)). - Stefano Spezia, Apr 16 2024 EXAMPLE a(2) = 19 as k = 19 is the two digit number k that produces the largest ratio R(k)/k = 91/19 of all two-digit numbers. MATHEMATICA Table[10^(n-1) + 10^Floor[n/2] - 1, {n, 25}] (* Paolo Xausa, Apr 23 2024 *) PROG (PARI) a(n) = 10^(n-1) + 10 ^ (n \ 2) - 1 (Python) def a(n): return 10**(n-1) + 10**(n//2) - 1 CROSSREFS Cf. A004086. Sequence in context: A144246 A281170 A158715 * A186105 A080442 A033655 Adjacent sequences: A372007 A372008 A372009 * A372011 A372012 A372013 KEYWORD nonn,easy AUTHOR David A. Corneth and Michael S. Branicky, Apr 15 2024 STATUS approved

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Last modified August 14 12:42 EDT 2024. Contains 375164 sequences. (Running on oeis4.)