A034003 -id:A034003 - cp's OEIS frontend

A007890 Summarize the previous term! (in decreasing order).

1, 11, 21, 1211, 1231, 131221, 132231, 232221, 134211, 14131231, 14231241, 24132231, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221, 14233221

Offset: 1

Mira Bernstein

			For example, the term after 131221 is obtained by saying "one 3, two 2's, three 1's", which gives 13-22-31, i.e. 132231.

Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.

Cf. A005150, A034003, A036058, A244112.

Nest[Append[#, FromDigits@ Flatten@ Map[Reverse, Tally@ ReverseSort@ IntegerDigits@ #[[-1]] ] ] &, {1}, 24] (* Michael De Vlieger, Jul 15 2020 *)

From Seiichi Manyama, Aug 18 2020: (Start)
a(1) = 1 and a(n) = A244112(a(n-1)) for n > 1.
a(n) = 14233221 for n >= 13. (End)

A083671 Array read by rows in which each row describes in words the composition of the previous row.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 2, 1, 3, 3, 1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 3, 1, 1, 4, 2, 1, 3, 3, 1, 1, 2, 1, 3, 1, 4, 4, 1, 1, 2, 2, 3, 1, 4, 3, 1, 2, 2, 1, 3, 2, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4, 2, 1, 3, 2, 2, 3, 1, 4

Offset: 1

N. J. A. Sloane, based on a query from Chasity Engle, Jan 20 2004

Becomes periodic at row 13.

			Array begins:
1
1 1
2 1
1 1 1 2
3 1 1 2
2 1 1 2 1 3
3 1 2 2 1 3
2 1 2 2 2 3
1 1 4 2 1 3
3 1 1 2 1 3 1 4
4 1 1 2 2 3 1 4
3 1 2 2 1 3 2 4
2 1 3 2 2 3 1 4
Explanation: look at 3 1 1 2. What do you see? Two 1's, one 2 and one 3, so the next row is 2 1 1 2 1 3.

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Onno M. Cain and Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.

Similar to A005151. Cf. A005150, A034002, A034003.

NestList[Function[test, Flatten[{Count[test, # ], # } & /@ Union[test]]], {1}, 13]
RunLengthEncode[x_List ] := (Through[ { Length, First}[ #1 ] ] &) /@ Split[ Sort[ x ]]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[n_] := LookAndSay[ n, 1 ][[ n ]]; Flatten[ Table[ F[n], {n, 18}]] (* Robert G. Wilson v, Jan 22 2004 *)

G.f.: x*(x^67 -x^65 -x^63 +x^61 -x^59 +x^57 -x^55 +x^53 -x^49 -x^45 -x^44 -x^42 +3*x^41 -x^40 +2*x^38 -x^37 -x^36 +x^35 -x^34 -2*x^33 +2*x^32 -x^30 -x^28 +x^27 +2*x^26 -x^25 -x^24 -x^22 +x^20 -2*x^19 -2*x^18 +2*x^17 -x^13 -x^12 +x^11 -2*x^9 -x^8 -x^7 -x^6 -x^5 -x^4 -2*x^3 -x^2 -x -1) / (x^8-1). - Alois P. Heinz, Jul 25 2013

More terms from Wouter Meeussen and Robert G. Wilson v, Jan 22 2004

cp's OEIS Frontend

A007890 Summarize the previous term! (in decreasing order).

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