

A180011


a(n) = smallest k > 1 such that n and kn have the same digit sum


1



10, 10, 4, 10, 10, 4, 10, 10, 2, 10, 10, 10, 10, 10, 4, 10, 10, 2, 10, 10, 10, 10, 10, 10, 10, 10, 2, 10, 10, 4, 10, 10, 4, 10, 10, 2, 10, 10, 4, 10, 10, 10, 10, 10, 2, 10, 10, 4, 10, 10, 4, 10, 10, 2, 10, 10, 4, 10, 10, 4, 10, 10, 2, 10, 10, 4, 10, 10, 4, 10, 10, 2, 10, 10, 7, 10, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

2 <= a(n) <= 10
Every number from 2 through 10 is in the sequence. a(9) = 2, a(144) = 3, a(3) = 4, a(243) = 5, a(5553) = 6, a(75) = 7, a(1314) = 8, a(6876) = 9, a(1) = 10. n !== 0 (mod 3) ==> a(n) = 10


LINKS

D. W. Wilson, Table of n, a(n) for n=1..10000


MAPLE

Digit sum of 15 = 6. The next multiple of 15 with digit sum 6 = 4*15 = 60, so a(15) = 4.


MATHEMATICA

ds[n_]:=Module[{dsn=Total[IntegerDigits[n]], k=2}, While[dsn!=Total[ IntegerDigits[k n]], k++]; k]; Array[ds, 80] (* Harvey P. Dale, Jan 16 2012 *)


CROSSREFS

Sequence in context: A285781 A228245 A034078 * A275626 A071531 A276467
Adjacent sequences: A180008 A180009 A180010 * A180012 A180013 A180014


KEYWORD

base,easy,nonn


AUTHOR

David W. Wilson, Aug 06 2010


STATUS

approved



