

A078268


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


4



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
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OFFSET

1,3


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


LINKS

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


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


EXAMPLE

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


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 *)


PROG

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


CROSSREFS

Cf. A078267.
Sequence in context: A089942 A097409 A257556 * A124782 A106611 A025261
Adjacent sequences: A078265 A078266 A078267 * A078269 A078270 A078271


KEYWORD

base,frac,nonn


AUTHOR

Amarnath Murthy, Nov 24 2002


EXTENSIONS

Edited and extended by Henry Bottomley, Dec 08 2002
Incorrect formula removed by Jaroslav Krizek, Feb 05 2010


STATUS

approved



