A084021 -id:A084021 - cp's OEIS frontend

A109847 Least common multiple of n and its 9's complement.

8, 14, 6, 20, 20, 6, 14, 8, 0, 890, 88, 348, 1118, 1190, 420, 1328, 1394, 162, 1520, 1580, 546, 154, 1748, 600, 1850, 1898, 216, 1988, 2030, 690, 2108, 2144, 66, 2210, 2240, 252, 2294, 2318, 780, 2360, 2378, 798, 2408, 220, 270, 2438, 2444, 816, 2450, 2450

Offset: 1

Amarnath Murthy, Jul 06 2005

			a(2)=14 because 7=9-2 and lcm(2,7)=14
a(9)=lcm(0,9)=0. a(10)=lcm(89,10)=890.

Alois P. Heinz, Table of n, a(n) for n = 1..9999

Cf. A109848, A084021.

digs := proc(inp::integer) local resul,shiftinp : resul := 1 : shiftinp := iquo(inp,10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp,10) : od : RETURN(resul) : end: nin := proc(inp::integer) RETURN(10^digs(inp)-1-inp) : end : for n from 1 to 40 do comp := nin(n) ; #print(n,comp,lcm(n,comp)) ; printf("%d,",lcm(n,comp)) ; od : # R. J. Mathar, Mar 27 2006
# second Maple program:
a:= n-> ilcm((10^length(n)-1-n), n):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 22 2015

Array[LCM[#,10^IntegerLength[#]-1-#]&,50] (* Harvey P. Dale, Apr 17 2012 *)

Corrected and extended by R. J. Mathar, Mar 27 2006

More terms from Joshua Zucker, May 03 2006

A109848 Highest common factor of n and its 9's complement.

Original entry on oeis.org

1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 11, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 11, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 33, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 11, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 11, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 33, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 11, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 11, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 99, 1, 1, 3

Offset: 1

Amarnath Murthy, Jul 06 2005

			a(55)=11 because the 9's complement of 55 is 99 - 55 = 44 and the greatest common divisor of 44 and 55 is 11.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A109847, A084021.

digs := proc(inp::integer) local resul,shiftinp : resul := 1 : shiftinp := iquo(inp,10) : while shiftinp > 0 do resul := resul+1 : shiftinp := iquo(shiftinp,10) : od : RETURN(resul) : end: nin := proc(inp::integer) RETURN(10^digs(inp)-1-inp) : end : for n from 1 to 80 do comp := nin(n) ; #print(n,comp,gcd(n,comp)) ; printf("%d,",gcd(n,comp)) ; od : # R. J. Mathar, Mar 27 2006

hcf[n_]:=Module[{idn=IntegerDigits[n],c9},c9=FromDigits[PadRight[{}, Length[idn],9]-idn];GCD[n,c9]]; Array[hcf,110] (* Harvey P. Dale, Dec 18 2012 *)

Corrected and extended by R. J. Mathar, Mar 27 2006

More terms from Joshua Zucker, May 03 2006

A327266 Product of A325907(n) and its 9's complement.

Original entry on oeis.org

18, 2268, 22316868, 2222332266866868, 22222222333322316666886866866868, 2222222222222222333333332222332266666666888866866666886866866868

Offset: 1

Seiichi Manyama, Sep 15 2019

nonn

			a(1) =        3 *        6 =         18.
a(2) =       63 *       36 =        2268.
a(3) =     3363 *     6636 =      22316868.
a(4) = 66663363 * 33336636 =  2222332266866868.
-----------------------------------------------
a(1) =        18        =        18        - 2 *        0 +    0 * 10^1.
a(2) =       2268       =       2188       - 2 *       10 +    1 * 10^2.
a(3) =     22316868     =     22218888     - 2 *     1010 +   10 * 10^4.
a(4) = 2222332266866868 = 2222222188888888 - 2 * 11011010 + 1101 * 10^8.

Cf. A002283, A084021, A178630, A325907, A325910, A325493, A327294.

def A(n)
  a = [3, 6]
  b = ([[3]] + (1..n - 1).map{|i| [a[i % 2]] * (2 ** (i - 1))}).reverse.join.to_i
  b * (10 ** (2 ** (n - 1)) - 1 - b)
end
def A327266(n)
  (1..n).map{|i| A(i)}
end
p A327266(6)

a(n) = A084021(A325907(n)) = A325907(n) * (A002283(2^(n-1)) - A325907(n)).

a(n) = A327294(n) - 10^(2^(n-1)) = a(n) = (2 * 10^(2^n) - 3 * 10^(2^(n-1)) - 8)/9 - 2 * A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).

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A109847 Least common multiple of n and its 9's complement.

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A109848 Highest common factor of n and its 9's complement.

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A327266 Product of A325907(n) and its 9's complement.

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