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Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.
7

%I #30 Jun 28 2020 11:49:39

%S 0,10,1110,3110,132110,13123110,23124110,1413223110,1423224110,

%T 2413323110,1433223110,1433223110,1433223110,1433223110,1433223110,

%U 1433223110,1433223110,1433223110,1433223110,1433223110,1433223110

%N Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.

%C This kind of counting sequence is always eventually periodic with period 1, 2 or 3. - Herve Lehning (lehning(AT)noos.fr), Oct 01 2003

%H Herve Lehning, <a href="http://www.jstor.org/stable/2686893">Computer-aided or analytic proof?</a>, College Mathematics Journal, Vol. 21, No. 3, 1990, pp. 228-239.

%H <a href="/index/Con#constant">Index of eventually constant sequences</a>.

%F a(n+1) = A244112(a(n)), a(0) = 0. - _M. F. Hasler_, Feb 25 2018

%e The third term is 1110 because the second term contains one 1 and one 0.

%o (PARI) a(n)=if(n>9,1433223110,[0,10,1110,3110,132110,13123110,23124110,1413223110, 1423224110,2413323110][n+1]) \\ _Charles R Greathouse IV_, Jul 24 2012

%o (PARI) a(n,a=0)={for(k=1,n,a==(a=A244112(a))&&break);a} \\ _M. F. Hasler_, Feb 25 2018

%Y Cf. A007890 (same as this, starting at 1), A001155 (same as this, but using method A047842: by increasing digit value), A005150 (as before, starting at 1), A036059 ("fibonacci" based on this), A036066.

%K nonn,base,easy,nice

%O 0,2

%A _Floor van Lamoen_