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

0,2

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

Links

Table of n, a(n) for n=0..20.

Herve Lehning, Computer-aided or analytic proof?, College Mathematics Journal, Vol. 21, No. 3, 1990, pp. 228-239.

Rosetta Code, Summarize and say sequence. Links to this sequence.

Index of eventually constant sequences.

Formula

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

Example

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

Mathematica

PadRight[#, 30, #[[-1]]] &@ FixedPointList[FromDigits@ Flatten@ ReverseSortBy[Map[Reverse, Tally@ IntegerDigits[#] ], Last] &, 0] (* Michael De Vlieger, Sep 14 2025 *)

Prog

(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

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.

Sequence in context: A204577 A210995 A325910 * A001155 A001391 A049064

Adjacent sequences: A036055 A036056 A036057 * A036059 A036060 A036061

Keyword

nonn,base,easy,nice

Author

Floor van Lamoen

Status

approved