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

Author

Amarnath Murthy, Nov 24 2002

Keywords

• base
• frac
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A078267.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Formula

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

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

Extensions

Edited and extended by Henry Bottomley, Dec 08 2002

Incorrect formula removed by Jaroslav Krizek, Feb 05 2010