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A073053
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Apply DENEAT operator to n.
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5
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11, 101, 11, 101, 11, 101, 11, 101, 11, 112, 22, 112, 22, 112, 22, 112, 22, 112, 22, 202, 112, 202, 112, 202, 112, 202, 112, 202, 112, 112, 22, 112, 22, 112, 22, 112, 22, 112, 22, 202, 112, 202, 112, 202, 112, 202, 112, 202, 112, 112, 22, 112, 22
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| DENEAT(n): concatenate number of even digits in n, number of odd digits and total number of digits. E.g. 25 -> 1.1.2 = 112 (Digits: Even, Not Even, And Total). Leading zeros are then omitted.
Repeated application of the DENEAT operator reduces all numbers to 123. This is easy to prove. Compare A100961. - N. J. A. Sloane (njas(AT)research.att.com) Jun 18 2005
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REFERENCES
| M. Ecker, Caution: Black Holes at Work, New Scientist (Dec. 1992)
M. J. Halm, Blackholing, Mpossibilities 69, (Jan 01 1999), p. 2.
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EXAMPLE
| a(1) = 0.1.1 -> 11.
a(10000000000) = 10111 because 10000000000 has 10 even digits, 1 odd digit and 11 total digits
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MATHEMATICA
| f[n_] := Block[{id = IntegerDigits[n]}, FromDigits[ Join[ IntegerDigits[ Length[ Select[id, EvenQ[ # ] &]]], IntegerDigits[ Length[ Select[id, OddQ[ # ] &]]], IntegerDigits[ Length[ id]] ]]]; Table[ f[n], {n, 0, 55}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2005)
s={}; Do[id=IntegerDigits[n]; ev=Select[id, EvenQ]; ne=Select[id, OddQ]; fd=FromDigits[{Length[ev], Length[ne], Length[id]}]; s=Append[s, fd], {n, 81}]; SameQ[newA073053-s] (Zak Seidov)
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CROSSREFS
| Cf. A008577, A072420, A073054, A100961.
Sequence in context: A127806 A036929 A168586 * A185121 A133835 A175963
Adjacent sequences: A073050 A073051 A073052 * A073054 A073055 A073056
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KEYWORD
| easy,nonn,base
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AUTHOR
| Michael Joseph Halm (hierogamous(AT)lycos.com), Aug 16 2002
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EXTENSIONS
| Edited and corrected by Jason Earls (zevi_35711(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 03 2005
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