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A234932 The product a(n)*a(n+1) can be written using the digits of {a(n),a(n+1)}; always choose the smallest possible unused positive integer. 4

%I

%S 1,2,10,3,51,30,100,4,16,40,160,352,151,34,106,25,13,24,26,240,130,

%T 250,133,295,313,1000,5,19,50,102,6,21,60,127,171,241,175,109,45,181,

%U 450,187,400,166,3052,1196,302,2865,1441,298,31,1165,139,7,1015,70,1043,700,1168,412,1702,125

%N The product a(n)*a(n+1) can be written using the digits of {a(n),a(n+1)}; always choose the smallest possible unused positive integer.

%C Inspired by A228276.

%H Reinhard Zumkeller, <a href="/A234932/b234932.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/WriteAB.htm">Add A to B</a>

%H E. Angelini, <a href="/A228276/a228276.pdf">Add A to B</a> [Cached copy, with permission]

%e 1*2 = 2 uses only digits from {1,2},

%e 2*10 = 20 uses only digits from {2,1,0},

%e 10*3 = 30 uses only digits from {1,0,3}.

%e What comes after 3? Call it x. 3*x must use only digits from 3 and the digits of x. Surprisingly x=51 is the first (unused) number which works.

%e And so on.

%o (Haskell)

%o import Data.List ((\\), delete)

%o a234932 n = a234932_list !! (n-1)

%o a234932_list = 1 : f 1 [2..] where

%o f x zs = g zs where

%o g (y:ys) = if null $ show (x * y) \\ (show x ++ show y)

%o then y : f y (delete y zs) else g ys

%o -- _Reinhard Zumkeller_, Jul 26 2014

%Y Cf. A228276

%K nonn,base,nice

%O 1,2

%A _Claudio Meller_, Jan 01 2014

%E Entered by _N. J. A. Sloane_ on _Claudio Meller_'s behalf and submitted for the 2014 JMM competition with his permission.

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)