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A087303 Smallest nontrivial multiple of n whose digit sum is the same as that of the digit sum of n. By nontrivial one means a(n) is not equal to n or (10^k)*n. 0 if no such number exists. 0
110, 12, 112, 140, 24, 133, 152, 18, 0, 1001, 300, 2002, 1022, 60, 304, 323, 36, 361, 1100, 10101, 1012, 11201, 312, 700, 1430, 54, 532, 551, 120, 120001, 10112, 132, 4012, 1610, 72, 703, 722, 156, 1120, 10004, 1050, 1204, 1232, 90, 1702, 1316, 192 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(10^k) does not exist, where k is any positive integer. - Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005

Dartyge, Luca, & Stanica show that a(n) = 0 iff n is a power of 10. - Charles R Greathouse IV, Oct 23 2009

LINKS

Table of n, a(n) for n=2..48.

Cecile Dartyge, Florian Luca and Pantelimon Stanica, On digit sums of multiples of an integer, Journal of Number Theory, 129 (2009), 2820-2830. [From Parthasarathy Nambi, Aug 22 2009]

EXAMPLE

a(21) = 10101 = 481*21.

PROG

(PARI) ispow10(n)=my(k); ispower(n, , &k); k==10||n==1||n==10

a(n)=my(k, s); if(ispow10(n), 0, s=sumdigits(k=n); while(sumdigits(k+=n)!=s||ispow10(k/n), ); k) \\ Charles R Greathouse IV, Feb 04 2013

CROSSREFS

Sequence in context: A282074 A282325 A266660 * A045884 A247391 A110736

Adjacent sequences:  A087300 A087301 A087302 * A087304 A087305 A087306

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Sep 01 2003

EXTENSIONS

More terms from Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 13 2005

STATUS

approved

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Last modified April 5 20:21 EDT 2020. Contains 333260 sequences. (Running on oeis4.)