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A187824 a(n) is the largest m such that n is congruent to -1, 0 or 1 mod k for all k from 1 to m. 11
3, 4, 5, 6, 3, 4, 4, 5, 3, 6, 4, 4, 3, 5, 5, 4, 3, 6, 5, 5, 3, 4, 6, 6, 3, 4, 4, 7, 3, 6, 4, 4, 3, 7, 7, 4, 3, 5, 5, 8, 3, 4, 5, 5, 3, 4, 4, 8, 3, 5, 4, 4, 3, 9, 5, 4, 3, 6, 6, 6, 3, 4, 5, 6, 3, 4, 4, 5, 3, 10, 4, 4, 3, 5, 5, 4, 3, 6, 5, 5, 3, 4, 7, 7, 3, 4, 4, 6, 3, 7, 4, 4, 3, 6, 6, 4, 3, 5, 5, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

This sequence and A187771 and A187761 are winners in the contest held at the 2013 AMS/MAA Joint Mathematics Meetings. - T. D. Noe, Jan 14 2013

If n = t!-1 then a(n) >= t, so sequence is unbounded. - N. J. A. Sloane, Dec 30 2012

First occurrence of k = 3, 4, 5,...:  2, 3, 4, 5, 29, 41, 55, 71, 881, 791, 9360, 10009, 1079, 30239, (17 unknown), 246960, (19 unknown), 636481, 1360800, 3160079, (23 unknown), 2162161, 266615999, 39412801  (27 unknown), 107881201,.... Searched up to 3*10^9. - Robert G. Wilson v, Dec 31 2012

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 2..10000

FORMULA

If n == 0 (mod 20), then a(n-2) = a(n+2) = 3, while a(n) = 5,5,6, 5,5,8, 5,5,6, 5,5,6, 5,5,7, 5,5,6, 5,5,7, ... with records a(20) = 5, a(60) = 6, a(120) = 8, a(720) = 10, a(2520)= 12, a(9360) = 13,... If n == 0(mod 5), but is not multiple of 20, then always a(n-2) = a(n+2) = 4, while a(n) = 6,3,5, 6,3,7, 5,3,9, 6,3,5, 7,3,6, 5,3,6, 7,3,5, ... - Vladimir Shevelev, Dec 31 2012

a(n)=3 iff n=2 (mod 4). a(n)=4 iff n=3, 7, 8, 12, 13, 17 (mod 20), i.e. n=2 or 3 (mod 5) but not n=2 (mod 4). In the same way one can obtain a covering set for any value taken by a(n), this is actually nothing else than the definition. For example, n=2, 3 or 4 (mod 6) but not 2 or 3 (mod 5) nor 2 (mod 4) yields a(n)=5 iff n=4, 9, 15, 16, 20, 21, 39, 40, 44, 45, 51 or 56 (mod 60), etc. - M. F. Hasler, Dec 31 2012

EXAMPLE

For n = 6, a(6) = 3 as follows.

m    Residue of 6 (mod m)

1             0

2             0

3             0

4             2

5             1

6             0

7            -1

MAPLE

A187824:= proc(n)

   local j, r;

   for j from 4 do

     r:= mods(n, j);

     if r <> r^3 then return j-1 end if

   end do

end proc; // Robert Israel, Dec 31 2012

MATHEMATICA

f[n_] := Block[{k = 4, r}, While[r = Mod[n, k]; r < 2 || k - r < 2, k++]; k - 1]; Array[f, 101, 2] (* Robert G. Wilson v, Dec 31 2012 *)

PROG

(Small Basic)

For n = 1 To 100

  For m = 1 To 100

  i = Math.Round(n/m)

  d = Math.Abs(n-i*m)

  If d > 1 Then

    a = m - 1

        Goto OUT

   Else

   EndIf

  EndFor

OUT:

TextWindow.Write(n+" ")

   TextWindow.Write(a+" ")

   TextWindow.WriteLine(" ")

EndFor

(PARI) A187824(n)={n>1 & for(k=4, 9e9, (n+1)%k>2&return(k-1))} \\ M. F. Hasler, Dec 31 2012

(PARI) a(n)=my(k=3); n++; while(n%k++<3, ); k-1 \\ Charles R Greathouse IV, Jan 02 2013

(Python)

from gmpy2 import t_mod

def A187824(n):

....k = 1

....while t_mod(n+1, k) < 3:

........k += 1

....return k-1 # Chai Wah Wu, Aug 31 2014

(Python)

def a(n):

..m=1

..while abs(n%m) < 2:

....m += 1

..return m

n = 1

while n < 100:

..print(n, end=', ')

..n += 1

# Derek Orr, Aug 31 2014

CROSSREFS

For values of n which set a new record see A220891. For smallest inverse see A220890 and A056697.

Sequence in context: A185383 A004484 A176210 * A177028 A162552 A133575

Adjacent sequences:  A187821 A187822 A187823 * A187825 A187826 A187827

KEYWORD

nonn,nice

AUTHOR

Kival Ngaokrajang, Dec 27 2012

EXTENSIONS

Corrected m = 100 by Kival Ngaokrajang, Dec 30 2012

Definition & example corrected by Kival Ngaokrajang, Dec 30 2012

More terms from N. J. A. Sloane, Dec 30 2012

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.