A073053 Apply DENEAT operator (or the Sisyphus function) to n.
101, 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
Offset: 0
Examples
a(1) = 0.1.1 -> 11. a(10000000000) = 10111 because 10000000000 has 10 even digits, 1 odd digit and 11 total digits
References
- M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.
- M. Ecker, Caution: Black Holes at Work, New Scientist (Dec. 1992)
- M. J. Halm, Blackholing, Mpossibilities 69, (Jan 01 1999), p. 2.
- J. Schram, The Sisyphus string, J. Rec. Math., 19:1 (1987), 43-44.
- M. Zeger, Fatal attraction, Mathematics and Computer Education, 27:2 (1993), 118-123.
Links
- N. J. A. Sloane, Table of n, a(n) for n = 0..20000
Crossrefs
Programs
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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 # Maple code based on R. J. Mathar's code for A171797, added by N. J. A. Sloane, May 12 2019 (Start) nevenDgs := proc(n) local a, d; a := 0 ; for d in convert(n, base, 10) do if type(d, 'even') then a :=a +1 ; end if; end do; a ; end proc: cat2 := proc(a, b) local ndigsb; ndigsb := max(ilog10(b)+1, 1) ; a*10^ndigsb+b ; end: catL := proc(L) local a, i; a := op(1, L) ; for i from 2 to nops(L) do a := cat2(a, op(i, L)) ; end do; a; end proc: A055642 := proc(n) max(1, ilog10(n)+1) ; end proc: A171797 := proc(n) local n1, n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n1, n2, n1-n2]) ; end proc: A073053 := proc(n) local n1, n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n2, n1-n2, n1]) ; end proc: seq(A073053(n), n=1..80) ; (End) L:=proc(n) if n=0 then 1 else floor(evalf(log(n)/log(10)))+1; fi; end; S:=proc(n) local Le,Ld,Lt,t1,e,d,t; global L; t1:=convert(n,base,10); e:=0; d:=0; t:=nops(t1); for i from 1 to t do if (t1[i] mod 2) = 0 then e:=e+1; else d:=d+1; fi; od: Le:=L(e); Ld:=L(d); Lt:=L(t); if e=0 then 10^Lt*d+t elif d=0 then 10^(Ld+Lt)*e+10^Lt*d+t else 10^(Ld+Lt)*e+10^Lt*d+t; fi; end; [seq(S(n),n=1..200)]; # N. J. A. Sloane, Jun 25 2018 # alternative Maple program: a:= n-> (l-> (e-> parse(cat(e, (h-> [h-e, h][])(nops(l)))) )(nops(select(x-> x::even, l))))(convert(n, base, 10)): seq(a(n), n=0..200); # Alois P. Heinz, Jan 21 2022 -
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 *) deneat[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Flatten[ IntegerDigits/@ {Count[ idn,?EvenQ],Count[ idn,?OddQ],Length[ idn]}]]] Array[ deneat,60,0]// Flatten (* Harvey P. Dale, Aug 13 2021 *) -
Python
def a(n): s = str(n) e = sum(1 for c in s if c in "02468") return int(str(e) + str(len(s)-e) + str(len(s))) print([a(n) for n in range(54)]) # Michael S. Branicky, Jan 21 2022
Extensions
Edited and corrected by Jason Earls and Robert G. Wilson v, Jun 03 2005
a(0) added by N. J. A. Sloane, May 12 2019
Comments