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Products of any two not necessarily distinct terms of A237424.
6

%I #14 Nov 12 2024 22:17:33

%S 1,4,7,16,28,34,37,49,67,136,148,238,259,268,334,337,367,469,667,1156,

%T 1258,1336,1348,1369,1468,2278,2338,2359,2479,2569,2668,3334,3337,

%U 3367,3667,4489,4669,6667,11356,11458,12358,12469,12478,13336,13348,13468,13579

%N Products of any two not necessarily distinct terms of A237424.

%C Digits are in nondecreasing order for all terms in decimal representation;

%C a(396) = 1123456789 = 3367 * 333667 is the smallest term containing all nonzero decimal digits: A254323(396) = 123456789;

%C A254323(n) = A137564(a(n)).

%H Reinhard Zumkeller, <a href="/A254143/b254143.txt">Table of n, a(n) for n = 1..10000</a>

%H Reinhard Zumkeller, <a href="/A254143/a254143.txt">First 10000 products of any two terms of A237424</a>

%e Initial terms of A237424: 1, 4, 7, 34, 37, 67, 334, 337, 367, 667, 3334 ...

%e . n | a(n) = A237424(i) * A237424(j)

%e . ---+-------------------------------

%e . 1 | 1 = 1 * 1 = A237424(1)^2

%e . 2 | 4 = 1 * 4 = A237424(1) * A237424(2)

%e . 3 | 7 = 1 * 7 = A237424(1) * A237424(3)

%e . 4 | 16 = 4 * 4 = A237424(2)^2

%e . 5 | 28 = 4 * 7 = A237424(2) * A237424(3)

%e . 6 | 34 = 1 * 34 = A237424(1) * A237424(4)

%e . 7 | 37 = 4 * 37 = A237424(1) * A237424(5)

%e . 8 | 49 = 7 * 7 = A237424(3)^2

%e . 9 | 67 = 1 * 67 = A237424(1) * A237424(6)

%e . 10 | 136 = 4 * 34 = A237424(2) * A237424(4)

%e . 11 | 148 = 4 * 37 = A237424(2) * A237424(5)

%e . 12 | 238 = 7 * 34 = A237424(3) * A237424(4)

%e . 13 | 259 = 7 * 37 = A237424(3) * A237424(5)

%e . 14 | 268 = 4 * 67 = A237424(2) * A237424(6)

%e . 15 | 334 = 1 * 334 = A237424(1) * A237424(7)

%e . 16 | 337 = 1 * 337 = A237424(1) * A237424(8)

%e . 17 | 367 = 1 * 367 = A237424(1) * A237424(9)

%e . 18 | 469 = 7 * 67 = A237424(3) * A237424(6)

%e . 19 | 667 = 1 * 34 = A237424(1) * A237424(10)

%e . 20 | 1156 = 34 * 34 = A237424(4)^2

%e see link for more.

%o (Haskell)

%o import Data.Set (empty, fromList, deleteFindMin, union)

%o import qualified Data.Set as Set (null)

%o a254143 n = a254143_list !! (n-1)

%o a254143_list = f a237424_list [] empty where

%o f xs'@(x:xs) zs s

%o | Set.null s || x < y = f xs zs' (union s $ fromList $ map (* x) zs')

%o | otherwise = y : f xs' zs s'

%o where zs' = x : zs

%o (y, s') = deleteFindMin s

%o (PARI) listA237424(lim)=my(v=List(),a,t); while(1, for(b=0,a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++)

%o list(lim)=my(v=List(),u=listA237424(lim),t); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim,break); listput(v,t))); Set(v) \\ _Charles R Greathouse IV_, May 13 2015

%Y Subsequence of A009994.

%Y Cf. A237424, A254323, A137564, A254338 (initial digits), A254339 (final digits).

%K nonn,changed

%O 1,2

%A _Reinhard Zumkeller_, Jan 28 2015