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 A070198 Smallest nonnegative number m such that m == i (mod i+1) for all 1 <= i <= n. 9
 0, 1, 5, 11, 59, 59, 419, 839, 2519, 2519, 27719, 27719, 360359, 360359, 360359, 720719, 12252239, 12252239, 232792559, 232792559, 232792559, 232792559, 5354228879, 5354228879, 26771144399, 26771144399, 80313433199, 80313433199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also, smallest k such that, for 0 <= i < n, i+1 divides k-i. Suggested by Chinese Remainder Theorem. This sequence can generate others: smallest b(n) such that b(n) == i (mod (i+2)), 1 <= i <= n, gives b(1)=1 and b(n) = a(n+1)-1 for n > 1; smallest c(n) such that c(n) == i (mod (i+3)), 1 <= i <= n, gives c(1)=1, c(2)=17 and c(n) = a(n+2) - 2 for n > 2; smallest d(n) such that c(n) == i (mod (i+4)), 1 <= i <= n, gives d(1)=1, d(2)=26, d(3)=206 and d(n) = a(n+3) - 3 for n > 3, etc. A208768(n) occurs A057820(n) times. - Reinhard Zumkeller, Mar 01 2012 From Kival Ngaokrajang, Oct 10 2013: (Start) A070198(n-1) is m such that max(Sum_{i=1..n} m (mod i)) = A000217(n-1). Example for n = 3:   m\i = 1  2  3  sum   1     0  1  1   2   2     0  0  2   2   3     0  1  0   1   4     0  0  1   1   5     0  1  2   3 <--max remainder sum = 3 = A000217(2)   6     0  0  0   0  first occuring at m = 5 = A070198(2) (End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Chinese Remainder Theorem Wikipedia, Chinese remainder theorem FORMULA a(n) = lcm(1, 2, 3, ..., n+1) - 1 = A003418(n+1) - 1. EXAMPLE a(3) = 11 because 11 == 1 (mod 2), 11 == 2 (mod 3) and 11 == 3 (mod 4). MAPLE seq(ilcm(\$1..n) - 1, n=1..100); # Robert Israel, Nov 03 2014 MATHEMATICA f[n_] := ChineseRemainder[ Range[0, n - 1], Range[n]]; Array[f, 28] (* or *) f[n_] := LCM @@ Range@ n - 1; Array[f, 28] (* Robert G. Wilson v, Oct 30 2014 *) PROG (Haskell) a070198 n = a070198_list !! n a070198_list = map (subtract 1) \$ scanl lcm 1 [2..] -- Reinhard Zumkeller, Mar 01 2012 (MAGMA) [Exponent(SymmetricGroup(n))-1 : n in [1..30]]; /* Vincenzo Librandi, Oct 31 2014 - after Arkadiusz Wesolowski in A003418 */ CROSSREFS Cf. A053664, A072562. Cf. A057825 (indices of primes). - R. J. Mathar, Jan 14 2009 Cf. A116151. - Zak Seidov, Mar 11 2014 Sequence in context: A192428 A060358 A091798 * A121934 A153812 A269454 Adjacent sequences:  A070195 A070196 A070197 * A070199 A070200 A070201 KEYWORD easy,nonn AUTHOR Benoit Cloitre, May 06 2002 EXTENSIONS Edited by N. J. A. Sloane, Nov 18 2007, at the suggestion of Max Alekseyev STATUS approved

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Last modified October 20 08:05 EDT 2019. Contains 328252 sequences. (Running on oeis4.)