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A073053 Apply DENEAT operator to n. 6
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; text; internal format)
OFFSET

1,1

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 Jun 18 2005

REFERENCES

M. Ecker, Caution: Black Holes at Work, New Scientist (Dec. 1992)

M. J. Halm, Blackholing, Mpossibilities 69, (Jan 01 1999), p. 2.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

a(1) = 0.1.1 -> 11.

a(10000000000) = 10111 because 10000000000 has 10 even digits, 1 odd digit and 11 total digits

DENEAT(1356)-> "1" even (6), "3" odd (1,3,5), "4" total digits ->134.

DENEAT(1490)-> "2" even (0 is considered even,4), "2" odd (1,9), "4" total digits -> 224. - Paolo P. Lava, Mar 05 2010

MAPLE

read("transforms") :

A073053 := proc(n)

    local e, o, L ;

    if n = 0 then

        0 ;

    else

        e := A196563(n) ;

        o := A196564(n) ;

        L := [e, o, e+o] ;

        digcatL(L) ;

    end if;

end proc: # R. J. Mathar, Jul 13 2012

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}] (* Robert G. Wilson v, 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 *)

CROSSREFS

Cf. A008577, A072420, A073054, A100961.

Sequence in context: A266515 A036929 A168586 * A185121 A133835 A225534

Adjacent sequences:  A073050 A073051 A073052 * A073054 A073055 A073056

KEYWORD

easy,nonn,base

AUTHOR

Michael Joseph Halm, Aug 16 2002

EXTENSIONS

Edited and corrected by Jason Earls (zevi_35711(AT)yahoo.com) and Robert G. Wilson v, Jun 03 2005

STATUS

approved

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Last modified May 23 08:03 EDT 2017. Contains 286909 sequences.