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A254143 Products of any two not necessarily distinct terms of A237424.

%I A254143 #14 Nov 12 2024 22:17:33
%S A254143 1,4,7,16,28,34,37,49,67,136,148,238,259,268,334,337,367,469,667,1156,
%T A254143 1258,1336,1348,1369,1468,2278,2338,2359,2479,2569,2668,3334,3337,
%U A254143 3367,3667,4489,4669,6667,11356,11458,12358,12469,12478,13336,13348,13468,13579
%N A254143 Products of any two not necessarily distinct terms of A237424.
%C A254143 Digits are in nondecreasing order for all terms in decimal representation;
%C A254143 a(396) = 1123456789 = 3367 * 333667 is the smallest term containing all nonzero decimal digits: A254323(396) = 123456789;
%C A254143 A254323(n) = A137564(a(n)).
%H A254143 Reinhard Zumkeller, <a href="/A254143/b254143.txt">Table of n, a(n) for n = 1..10000</a>
%H A254143 Reinhard Zumkeller, <a href="/A254143/a254143.txt">First 10000 products of any two terms of A237424</a>
%e A254143 Initial terms of A237424: 1, 4, 7, 34, 37, 67, 334, 337, 367, 667, 3334 ...
%e A254143 .  n | a(n) = A237424(i) * A237424(j)
%e A254143 . ---+-------------------------------
%e A254143 .  1 |    1 = 1 * 1   = A237424(1)^2
%e A254143 .  2 |    4 = 1 * 4   = A237424(1) * A237424(2)
%e A254143 .  3 |    7 = 1 * 7   = A237424(1) * A237424(3)
%e A254143 .  4 |   16 = 4 * 4   = A237424(2)^2
%e A254143 .  5 |   28 = 4 * 7   = A237424(2) * A237424(3)
%e A254143 .  6 |   34 = 1 * 34  = A237424(1) * A237424(4)
%e A254143 .  7 |   37 = 4 * 37  = A237424(1) * A237424(5)
%e A254143 .  8 |   49 = 7 * 7   = A237424(3)^2
%e A254143 .  9 |   67 = 1 * 67  = A237424(1) * A237424(6)
%e A254143 . 10 |  136 = 4 * 34  = A237424(2) * A237424(4)
%e A254143 . 11 |  148 = 4 * 37  = A237424(2) * A237424(5)
%e A254143 . 12 |  238 = 7 * 34  = A237424(3) * A237424(4)
%e A254143 . 13 |  259 = 7 * 37  = A237424(3) * A237424(5)
%e A254143 . 14 |  268 = 4 * 67  = A237424(2) * A237424(6)
%e A254143 . 15 |  334 = 1 * 334 = A237424(1) * A237424(7)
%e A254143 . 16 |  337 = 1 * 337 = A237424(1) * A237424(8)
%e A254143 . 17 |  367 = 1 * 367 = A237424(1) * A237424(9)
%e A254143 . 18 |  469 = 7 * 67  = A237424(3) * A237424(6)
%e A254143 . 19 |  667 = 1 * 34  = A237424(1) * A237424(10)
%e A254143 . 20 | 1156 = 34 * 34 = A237424(4)^2
%e A254143 see link for more.
%o A254143 (Haskell)
%o A254143 import Data.Set (empty, fromList, deleteFindMin, union)
%o A254143 import qualified Data.Set as Set (null)
%o A254143 a254143 n = a254143_list !! (n-1)
%o A254143 a254143_list = f a237424_list [] empty where
%o A254143    f xs'@(x:xs) zs s
%o A254143      | Set.null s || x < y = f xs zs' (union s $ fromList $ map (* x) zs')
%o A254143      | otherwise           = y : f xs' zs s'
%o A254143      where zs' = x : zs
%o A254143            (y, s') = deleteFindMin s
%o A254143 (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 A254143 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 A254143 Subsequence of A009994.
%Y A254143 Cf. A237424, A254323, A137564, A254338 (initial digits), A254339 (final digits).
%K A254143 nonn
%O A254143 1,2
%A A254143 _Reinhard Zumkeller_, Jan 28 2015