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Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.
16

%I #23 Jan 25 2024 07:53:49

%S 0,11,13,17,18,25,28,54,55,64,65,112,121,134,137,143,148,155,156,165,

%T 166,173,178,184,187,198,200,209,211,216,231,233,234,237,244,245,270,

%U 275,280,285,314,336,341,358,363,385,396,402,407,410,413,429,431,432

%N Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

%C Terms computed by Barry and Theunis de Jong.

%C Subsequence A036301 lists fixed points of the map f = A304439. - _M. F. Hasler_, May 18 2018

%H Eric Angelini, Dec 04 2006, <a href="/A124176/b124176.txt">Table of n, a(n) for n = 1..172</a>

%e 11 and 13 loop on themselves, but 12 doesn't:

%e 11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11

%e 12 -> 11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11

%e 13 -> 17 -> 25 -> 28 -> 18 -> 11 -> 13.

%o (PARI) is(n,S=List())=until(setsearch(Set(S),n=A304439(n)),listput(S,n));n==S[1] \\ _M. F. Hasler_, May 18 2018

%Y Cf. A124177, A036301, A304439; A071648, A071649, A071650.

%K base,easy,nonn

%O 1,2

%A _Eric Angelini_, Dec 04 2006