A098595 Roman numerals version of the Look and Say sequence (original at A005150).

1, 11, 111, 1111, 151, 111511, 111115111, 51151111, 1511115151, 111515115111511, 111115111511115111115111, 51151111151511551151111, 15111155115111511111511115151, 111515111511115111115511515115111511, 1111151115111115151155111511115111511115111115111, 511511111551151115111115111115151151111151511551151111

Offset

1,2

Comments

This sequence is suggested at the link given in point 7 at the bottom of the page, but it is given as: I, II, III, IIII, IIV, IIIIV, IVIIV, ... The 5th term seems to use the "number" followed by "frequency" method (one appears 4 times -> "I"//"IV") but the 6th and 7th terms use the usual "frequency"//"number" method.

The analog of Conway's constant for this sequence is C=1.09807850157..., the largest real root of x^17+x^16-x^14-x^13+x^11+x^10-x^8-x^7-x^6+x^4-x^2-x-1. - Ercole S. Banani, Jul 27 2023

Links

Table of n, a(n) for n=1..16.

T. Sillke, Conway sequence

Formula

We write the Roman numerals as I, II, III, IV, V and convert the letters into 1's and 5's for the inclusion in the encyclopedia.

Example

a(1)=I=1; a(2)="one I"="II"=11; a(3)=111; a(4)=1111; a(5)="four Is"="IVI"=151; and so on.

Mathematica

A098595[1] = 1; A098595[n_] := A098595[n] = FromDigits[Flatten[{Length[#1] /. {4->{1, 5}, 3->{1, 1, 1}, 2->{1, 1}}, First[#1]} &/@Split[IntegerDigits[A098595[n-1]]]]]; Map[A098595, Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

Crossrefs

Cf. A005150 for original Look and Say sequence and a number of references.

Sequence in context: A265380 A114397 A336325 * A273978 A334131 A077488

Adjacent sequences: A098592 A098593 A098594 * A098596 A098597 A098598

Keyword

base,easy,nonn

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 17 2004

Extensions

More terms from David Wasserman, Feb 25 2008

Status

approved