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Search: id:A078459
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| A078459 |
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Numbers n such that in some base b <= log n the sum of the digits of n in base b equals b. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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In base 4, 67=(1003)_4, and the sum 1+0+0+3 equals 4.
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MATHEMATICA
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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]
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CROSSREFS
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In a sense this generalizes the sequence A018900 (if b=2 is considered).
Sequence in context: A120185 A076364 A048592 this_sequence A078390 A037408 A116594
Adjacent sequences: A078456 A078457 A078458 this_sequence A078460 A078461 A078462
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KEYWORD
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nonn
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Dec 31 2002
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