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A190481
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Number of distinct integers with n digits which are the image of integers by the function Reverse and Add!.
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2
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4, 14, 93, 256, 1793, 4872, 34107, 92590, 648154, 1759313, 12315269, 33427272, 233991155, 635119194, 4445835138, 12067267861, 84470877438, 229278099157, 1604946701532, 4356283914175, 30493987422124, 82769394462323, 579385761306789, 1572618495070552
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OFFSET
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1,1
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COMMENTS
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a(n) is the cardinality of the set of Image(Reverse and Add!) intersected with [10^(n-1), 10^n[. Here we suppose that the domain of the function Reverse and Add! is {1, 2, 3, ...}
There are 4, 50, 450, 4590, 45405,... (A232731) ways to obtain integers with n = 1,2,... digits as images under the function "Reverse and add!", but many result in the same image and are counted here only once. Example: 11+digrev(11) = 22 and 20+digrev(20)=22 contribute only once to the set of distinct images at n=2. - R. J. Mathar, Jun 17 2011
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LINKS
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FORMULA
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Empirical g.f.: x*(4 + 18*x + 23*x^2 - 29*x^3 - 58*x^4 - 34*x^5 - 81*x^6 - 45*x^7 - 32*x^8 - 9*x^9) / ((1 + x)*(1 - 19*x^2)*(1 - 2*x + x^2 - x^3)*(1 + 2*x + x^2 + x^3)). - Colin Barker, Mar 20 2017
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EXAMPLE
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Example: let RaA(x) be the function Reverse and Add!, then:
RaA(1)=2
RaA(2)=4
RaA(3)=6
RaA(4)=8
RaA(5)=10
RaA(6)=11, ...
So a(1) is the cardinal of {2,4,6,8}, which is 4:
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MAPLE
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A055642 := proc(n) max(1, 1+ilog10(n)) ; end proc:
A056964 := proc(n) n+digrev(n) ; end proc:
A190481 := proc(n) local s, i, ra ; s := {} ; for i from 1 to 10^n do ra := A056964(i) ; if A055642( ra) = n then s := s union {ra} ; end if; end do: nops(s) ; end proc:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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