A180011 a(n) = smallest k > 1 such that n and kn have the same digit sum

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

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: A360207 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