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"Say what you see".
3

%I #24 Feb 24 2024 01:16:00

%S 3,13,1113,3113,2123,112213,312213,212223,114213,31121314,41122314,

%T 31221324,21322314,21322314,21322314,21322314,21322314,21322314,

%U 21322314,21322314,21322314,21322314,21322314,21322314,21322314,21322314,21322314,21322314,21322314

%N "Say what you see".

%H Madras College, <a href="http://www.madras.fife.sch.uk/departments/Mathematics/activities/descriptive%20numbers/descriptive6.html">Descriptive Numbers</a>

%F a(n) = 21322314 for n > 12; a(n) = A005151(n) for n > 6. - _Reinhard Zumkeller_, Jan 26 2014

%F a(n) = A047842(a(n-1)). - _Pontus von Brömssen_, Jun 04 2023

%e 3 = "one three" --> 13

%e 13 = "one one, one three" --> 1113

%e 1113 = "three ones, one three" --> 3113

%e 3113 = "two ones, two threes" --> 2123

%o (Haskell)

%o import Data.List (group, sort, transpose)

%o a118628 n = a118628_list !! (n-1)

%o a118628_list = 3 : f [3] :: [Integer] where

%o f xs = (read $ concatMap show ys) : f (ys) where

%o ys = concat $ transpose [map length zss, map head zss]

%o zss = group $ sort xs

%o -- _Reinhard Zumkeller_, Jan 26 2014

%Y Cf. A005151.

%Y Cf. A047842, A023989.

%K nonn

%O 1,1

%A _Parthasarathy Nambi_, May 09 2006