

A078459


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


0



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
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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 A216780
Adjacent sequences: A078456 A078457 A078458 * A078460 A078461 A078462


KEYWORD

nonn,base


AUTHOR

Carlos Alves, Dec 31 2002


STATUS

approved



