A022471 Length of n-th term of A022470.

1, 2, 4, 4, 6, 10, 12, 14, 22, 26, 30, 44, 56, 70, 98, 130, 162, 216, 292, 358, 470, 628, 792, 1050, 1384, 1788, 2334, 3072, 3974, 5162, 6784, 8786, 11420, 14992, 19484, 25388, 33160, 43262, 56252, 73392, 95798, 124496, 162556, 212048, 275976, 360154

Offset

1,2

Comments

From Clark Kimberling, Jun 14 2013: (Start)

a(n) is the length of the n-th term of many sequences generated by methods A and B, including those shown here:

Method A, 1st term ... Method B, 1st term

A001155, 0

A006751, 2 ......... A022470, 2

A006715, 3 ......... A022499, 3

A001140, 4 ......... A022500, 4

A001141, 5 ......... A022501, 5

A001143, 6 ......... A022502, 6

A001145, 7 ......... A022503, 7

A001151, 8 ......... A022504, 8

A001154, 9 ......... A022505, 9

(End)

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..3000

Eric Weisstein's World of Mathematics, Look and Say Sequence.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, -1, -3, 0, 1, 2, 0, 0, 0, 0, -3, -3, 2, 5, 8, -7, -1, -8, 0, 5, -8, 12, 4, 1, 0, -18, 4, -2, 13, 7, -19, 14, -14, 6, 4, -13, 9, 7, -4, 8, -7, -5, -7, 12, -17, 22, -8, 7, -16, 6, 7, 6, -3, -19, 5, 5, 14, -8, -2, -7, 5, -1, 8, -14, 11, -16, 18, -9, 9, -6).

Formula

a(n) = A055642(A022470(n)) = A055642(A006751(n)) = A055642(A006715(n)). - Zhuorui He, Sep 29 2025

Example

The 7th term of A022470 is 211222113113, so a(7) = 12. - Zhuorui He, Sep 29 2025

Mathematica

a[0] = 2; a[n_] := a[n] = FromDigits[Flatten[{First[#], Length[#]} & /@   Split[IntegerDigits[a[n - 1]]]]]; Map[Length[IntegerDigits[a[#]]] &, Range[0, 40]] (* Peter J. C. Moses, Jun 14 2013 *)
p = {9, -9, 6, -16, 5, 2, 0, -9, -1, -1, 20, 2, 6, -3, -15, -13, 15, 20, 15, -26, -28, 7, 6, 26, -27, -4, 9, -15, 3, 2, 8, 43, 9, -39, -24, -2, -24, 28, 9, 13, 13, -18, -12, -16, 14, 13, 16, 8, -36, 1, -6, -8, 15, 1, 14, 3, -6, -7, -3, 2, -2, 2, 2, 0, -1, -2, -1, 3, 3, -1, -1, -1}; q = {-6, 9, -9, 18, -16, 11, -14, 8, -1, 5, -7, -2, -8, 14, 5, 5, -19, -3, 6, 7, 6, -16, 7, -8, 22, -17, 12, -7, -5, -7, 8, -4, 7, 9, -13, 4, 6, -14, 14, -19, 7, 13, -2, 4, -18, 0, 1, 4, 12, -8, 5, 0, -8, -1, -7, 8, 5, 2, -3, -3, 0, 0, 0, 0, 2, 1, 0, -3, -1, 1, 1, 1, -1}; gf = Fold[x #1 + #2 &, 0, p]/Fold[x #1 + #2 &, 0, q]; CoefficientList[Series[gf, {x, 0, 100}], x] (* Peter J. C. Moses, Jun 16 2013 *)

Crossrefs

Cf. A022470, A005341, A006751, A006715.

Sequence in context: A362607 A340626 A351489 * A359294 A224487 A185342

Adjacent sequences: A022468 A022469 A022470 * A022472 A022473 A022474

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved