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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
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
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 A331523
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