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A308005
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A modified Sisyphus function: a(n) = concatenation of (number of odd digits in n) (number of digits in n) (number of even digits in n).
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2
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11, 110, 11, 110, 11, 110, 11, 110, 11, 110, 121, 220, 121, 220, 121, 220, 121, 220, 121, 220, 22, 121, 22, 121, 22, 121, 22, 121, 22, 121, 121, 220, 121, 220, 121, 220, 121, 220, 121, 220, 22, 121, 22, 121, 22, 121, 22, 121, 22, 121, 121, 220, 121, 220, 121, 220, 121, 220, 121, 220, 22, 121, 22, 121, 22
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OFFSET
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0,1
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COMMENTS
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If we start with n and repeatedly apply the map i -> a(i), it appears that we eventually reach one of the two fixed points 22 or 231, or enter the two-cycle (33, 220). Are there any other possibilities? This is in contrast to the behavior of the closely related A308003.
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REFERENCES
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M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.
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LINKS
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EXAMPLE
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11 has 2 digits, both odd, so a(11)=220.
12 has 2 digits, one even and one odd, so a(12)=121. Then a(121) = 231, a fixed point.
22 has two digits, both even, so 22 -> 22, another fixed point (leading zeros are omitted).
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MAPLE
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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:
A308005 := proc(n) local n1, n2 ; n1 := A055642(n) ; n2 := nevenDgs(n) ; catL([n1-n2, n1, n2]) ; end proc:
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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