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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

Index entries for sequences related to lcm's

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: A060358 A091798 * A121934 A153812 A269454 A153209

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 November 20 21:05 EST 2018. Contains 317422 sequences. (Running on oeis4.)