A068822 -id:A068822 - cp's OEIS frontend

A078268 Smallest integer which is an integer multiple of the number N obtained by placing the string "n" after a decimal point.

1, 1, 3, 2, 1, 3, 7, 4, 9, 1, 11, 3, 13, 7, 3, 4, 17, 9, 19, 1, 21, 11, 23, 6, 1, 13, 27, 7, 29, 3, 31, 8, 33, 17, 7, 9, 37, 19, 39, 2, 41, 21, 43, 11, 9, 23, 47, 12, 49, 1, 51, 13, 53, 27, 11, 14, 57, 29, 59, 3, 61, 31, 63, 16, 13, 33, 67, 17, 69, 7, 71, 18, 73, 37, 3, 19, 77, 39, 79

Offset: 1

Amarnath Murthy, Nov 24 2002

Numerator of n/10^k, where k is the number of digits in n. - Dean Hickerson, Mar 21 2003
a(p) = p if p is a prime other than 2 and 5.
Smallest integer m such that the concatenation of decimal representations of m and n is a multiple of n. - Reinhard Zumkeller, Mar 19 2003
a(n) = numerator of fraction a/b, where gcd(a, b) = 1, such that its decimal representation has the form 0.(n). Denominators in A078267: 10, 5, 10, 5, 2, 5, 10, 5, 10, 10, 100, ... Example: a(6) = 3; 3/5 = 0.6. - Jaroslav Krizek, Feb 05 2010
a(n) = n iff gcd(n,10) = 1. - Robert Israel, Jul 25 2014

			a(40)=2 since writing 40 after the decimal point gives 0.40 and 2 is the smallest integer multiple of 0.4.

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

Cf. A078267.

a:= n -> numer(n/10^(1+ilog10(n))):
seq(a(n),n=1..100); # Robert Israel, Jul 25 2014

si[n_]:=Module[{c=n/10^IntegerLength[n],m=1},While[!IntegerQ[c*m],m++]; c*m]; Array[si,80] (* Harvey P. Dale, Apr 06 2013 *)
Table[n/GCD[n, 10^(1 + Floor[Log10[n]])], {n, 79}] (* L. Edson Jeffery, Jul 25 2014 *)

a(n) = numerator(n/10^(#Str(n))); \\ Michel Marcus, Mar 31 2019

a(n) = n *A078267(n)/10^A055642(n). - Jaroslav Krizek, Feb 05 2010

a(n) = n/A068822(n). - L. Edson Jeffery, Jul 25 2014

Edited and extended by Henry Bottomley, Dec 08 2002

Incorrect formula removed by Jaroslav Krizek, Feb 05 2010

A214587 Greatest common divisor of a number and its last decimal digit: a(n) = gcd(n, n mod 10).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 20, 1, 2, 1, 4, 5, 2, 1, 4, 1, 30, 1, 2, 3, 2, 5, 6, 1, 2, 3, 40, 1, 2, 1, 4, 5, 2, 1, 8, 1, 50, 1, 2, 1, 2, 5, 2, 1, 2, 1, 60, 1, 2, 3, 4, 5, 6, 1, 4, 3, 70, 1, 2, 1, 2, 5, 2, 7, 2, 1, 80, 1, 2, 1, 4, 5

Offset: 0

Alex Ratushnyak, Jul 22 2012

			a(69) = gcd(69,9) = 3.

Cf. A068822.

import java.math.BigInteger;
public class A214587 {
  public static void main (String[] args) {
    for (long n=0; n<222; n++) {
    BigInteger bn=BigInteger.valueOf(n), ld=BigInteger.valueOf(n%10);
    System.out.printf("%s, ", bn.gcd(ld).toString());
    }
  }
}

Table[GCD[n, Mod[n, 10]], {n, 0, 100}] (* T. D. Noe, Jul 24 2012 *)

A068823 a(n) = lcm(n, c(n)), where c(n) is the 10's complement of n.

Original entry on oeis.org

9, 8, 21, 12, 5, 12, 21, 8, 9, 90, 979, 264, 1131, 602, 255, 336, 1411, 738, 1539, 80, 1659, 858, 1771, 456, 75, 962, 1971, 504, 2059, 210, 2139, 544, 2211, 1122, 455, 576, 2331, 1178, 2379, 120, 2419, 1218, 2451, 616, 495, 1242, 2491, 624, 2499, 50

Offset: 1

Amarnath Murthy, Mar 08 2002

			a(45) = 495 as 10's complement of 45 is 100 - 45 = 55 and lcm(45, 55) = 495.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A068822.

a:=n-> ilcm((10^length(n)-n), n):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 22 2015

LCM[#, 10^(IntegerLength[#]) - #] & /@ Range[50] (* Jayanta Basu, Aug 07 2013 *)

a(20) corrected by Jayanta Basu, Aug 07 2013

cp's OEIS Frontend

A078268 Smallest integer which is an integer multiple of the number N obtained by placing the string "n" after a decimal point.

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A214587 Greatest common divisor of a number and its last decimal digit: a(n) = gcd(n, n mod 10).

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Java

Mathematica

A068823 a(n) = lcm(n, c(n)), where c(n) is the 10's complement of n.

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Maple

Mathematica

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