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A329200
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The ghost iteration (A): add or subtract the number formed by absolute differences of digits (A040115), according to parity (even or odd).
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15
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 11, 11, 15, 11, 19, 11, 23, 11, 27, 22, 20, 22, 22, 26, 22, 30, 22, 34, 22, 27, 33, 31, 33, 33, 37, 33, 41, 33, 45, 44, 38, 44, 42, 44, 44, 48, 44, 52, 44, 45, 55, 49, 55, 53, 55, 55, 59, 55, 63, 66, 56, 66, 60, 66, 64, 66, 66, 70, 66, 63, 77, 67, 77, 71, 77
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history;
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OFFSET
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0,3
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COMMENTS
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Sequence A040115 is most naturally extended to 0 (empty sum) for single-digit arguments; that's what we use here. This value is added to n if even, subtracted if odd.
Repdigit numbers are the fixed points. Other starting values end in nontrivial loops under iterations of this map, like 11090 -> 10891 -> 12709 -> 11130 -> 11107 -> 11090 etc. Table A329196 lists these cycles, A329197 their lengths.
A329198 gives the size of n's orbit, i.e., the length of the trajectory until the terminating cycle is covered.
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LINKS
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FORMULA
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a(n) = n + (-1)^d*d where d = A040115(n), 0 for n < 10.
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EXAMPLE
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For n = 101, the number formed by the absolute differences of digits is 11, since this is odd it is subtracted from n, so a(101) = 101-11 = 90.
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PROG
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(PARI) apply( A329200(n)={n+(-1)^(n=fromdigits(abs((n=digits(n+!n))[^-1]-n[^1])))*n}, [1..199])
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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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