A329201 The ghost iteration (B): add or subtract the number formed by absolute differences of digits (A040115), according to parity (odd or even).

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

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

Table of n, a(n) for n=0..76.

E. Angelini, The ghost iteration, SeqFan list, Nov 2019.

E. Angelini, The ghost iteration, SeqFan list, Nov 2019 [Cached copy, with permission]

E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019.

E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019 [Cached copy, pdf file, with permission]

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: A381015 A355222 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