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

Author

Carlos Alves, Dec 31 2002

Keywords

• nonn
• base

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.

Examples

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

Crossrefs

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

Programs

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]