A078459 Numbers n such that in some base b <= log n the sum of the digits of n in base b equals b.

9, 10, 12, 17, 18, 20, 21, 24, 29, 31, 33, 34, 36, 37, 39, 40, 45, 48, 55, 57, 63, 65, 66, 67, 68, 70, 72, 73, 76, 80, 82, 83, 85, 87, 88, 91, 93, 96, 97, 99, 100, 109, 111, 112, 117, 129, 130, 132, 133, 135, 136, 144, 145, 148, 153, 157, 160, 161, 163, 165, 171, 177

Offset

1,1

Comments

The sequence A018900 refers to b=2. Other sequences with b=3,4,5,... could be considered separately. We present the case that includes the several b, provided that b<=Log(n) (this condition avoids trivial situations). - It is not completely clear how the sequence grows.

Links

Table of n, a(n) for n=1..62.

Example

In base 4, 67=(1003)_4 and the sum 1+0+0+3 equals 4.

Mathematica

Seq = Function[{m}, Module[{ls, sk}, ls = {}; Do[Do[ sk = Apply[Plus, IntegerDigits[k, b]]; If[sk == b && E^b <= k, AppendTo[ls, k]], {b, 2, Log[k]}], {k, 1, m}]; Union[Sort[ls]] ]]; Seq[1000]

Crossrefs

In a sense this generalizes the sequence A018900 (if b=2 is considered).

Sequence in context: A160947 A158581 A343258 * A156345 A078390 A354038

Adjacent sequences: A078456 A078457 A078458 * A078460 A078461 A078462

Keyword

nonn,base

Author

Carlos Alves, Dec 31 2002

Status

approved