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 A329201 The ghost iteration (B): add or subtract the number formed by absolute differences of digits (A040115), according to parity (odd or even). 10
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 13, 11, 17, 11, 21, 11, 25, 11, 18, 22, 22, 24, 22, 28, 22, 32, 22, 36, 33, 29, 33, 33, 35, 33, 39, 33, 43, 33, 36, 44, 40, 44, 44, 46, 44, 50, 44, 54, 55, 47, 55, 51, 55, 55, 57, 55, 61, 55, 54, 66, 58, 66, 62, 66, 66, 68, 66, 72, 77, 65, 77, 69, 77, 73, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence A040115 is most naturally extended to 0 (empty sum) for single digit arguments, that's what we use for n < 10 here. This value is subtracted from n if even, added if odd. A040115 is zero iff the argument is a repdigit (A010785), which therefore are the fixed points of this map A329201. All small starting values reach a fixed point, but larger values may enter a nontrivial cycle (or "loop"). See the table A329342 for the list of these cycles. LINKS E. Angelini, The ghost iteration, SeqFan list, Nov 2019 FORMULA a(n) = n - (-1)^d*d where d = A040115(n), 0 for n < 10. EXAMPLE For n = 101, the number formed by the absolute differences of digits is 11. Since this is odd it is added to n, so a(101) = 101 + 11 = 112. PROG (PARI) apply( A329201(n)={n-(-1)^(n=fromdigits(abs((n=digits(n+!n))[^-1]-n[^1])))*n}, [1..199]) CROSSREFS Cf. A040115, A329200 (variant A: add/subtract if even/odd), A010785 (fixed points). Cf. A329342 (list of cycles). Sequence in context: A262039 A123241 A033862 * A262038 A265558 A082273 Adjacent sequences:  A329198 A329199 A329200 * A329202 A329203 A329204 KEYWORD nonn,base,easy AUTHOR Eric Angelini and M. F. Hasler, Nov 09 2019 STATUS approved

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Last modified April 9 16:14 EDT 2020. Contains 333361 sequences. (Running on oeis4.)