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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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