A036058 Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.

0, 10, 1110, 3110, 132110, 13123110, 23124110, 1413223110, 1423224110, 2413323110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110

Offset: 0

Author

Floor van Lamoen

Keywords

• nonn
• base
• easy
• nice

Comments

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

Examples

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

Links

• Herve Lehning, Computer-aided or analytic proof?, College Mathematics Journal, Vol. 21, No. 3, 1990, pp. 228-239.
• Index of eventually constant sequences.

Crossrefs

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.

Programs

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

PARI

a(n,a=0)={for(k=1,n,a==(a=A244112(a))&&break);a} \\ M. F. Hasler, Feb 25 2018

Formula

a(n+1) = A244112(a(n)), a(0) = 0. - M. F. Hasler, Feb 25 2018