

A077196


Smallest possible sum of the digits of a multiple of n.


7



1, 1, 3, 1, 1, 3, 2, 1, 9, 1, 2, 3, 2, 2, 3, 1, 2, 9, 2, 1, 3, 2, 2, 3, 1, 2, 9, 2, 2, 3, 3, 1, 6, 2, 2, 9, 3, 2, 3, 1, 5, 3, 3, 2, 9, 2, 2, 3, 2, 1, 3, 2, 3, 9, 2, 2, 3, 2, 2, 3, 2, 3, 9, 1, 2, 6, 3, 2, 3, 2, 3, 9, 2, 3, 3, 2, 2, 3, 4, 1, 9, 5, 3, 3, 2, 3, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 2, 2, 18, 1, 2, 3, 2, 2, 3
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OFFSET

1,3


COMMENTS

a(n) is not bounded since a(10^n1)=9n. (Rustem Aidagulov)
In May 2002, this sequence (up to n=1000 with some useful remarks) was constructed by Pavel V. Phedotov. Some problems at the Second International Distant School Olympiad in Math "Third Millennium" (January 2002) asked to find a(n) for n = 5, 6, 7, 8, 9, 55, 66, 77, 88, 99, 555, 666, 777, 888, 999, and 2002^2002 .  Valery P. Phedotov (vphedotov(AT)narod.ru), May 05 2010


LINKS

A.V.Izvalov, S.T.Kuznetsov, Table of n, a(n) for n = 1..56000
Pavel V. Phedotov, Sum of digits of a multiple of a given number, May 2002. (in Russian)
Valery P. Phedotov, Problems from 2002 Math Olympiad "Third Millennium" (in Russian)


FORMULA

a(n) = A007953(A077194(n)).
a(2n)=a(n) and a(5n)=a(n) for any n. In particular, a(2^a*5^b) = a(1) = 1 where a or b are nonnegative integer.


CROSSREFS

Cf. A077194, A077195.
Sequence in context: A140216 A176514 A238559 * A023142 A225335 A229166
Adjacent sequences: A077193 A077194 A077195 * A077197 A077198 A077199


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Nov 01 2002


EXTENSIONS

More terms from Sascha Kurz, Feb 10 2003
Corrected and extended by Max Alekseyev, Feb 26 2009


STATUS

approved



