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A254143 Products of any two not necessarily distinct terms of A237424. 6
1, 4, 7, 16, 28, 34, 37, 49, 67, 136, 148, 238, 259, 268, 334, 337, 367, 469, 667, 1156, 1258, 1336, 1348, 1369, 1468, 2278, 2338, 2359, 2479, 2569, 2668, 3334, 3337, 3367, 3667, 4489, 4669, 6667, 11356, 11458, 12358, 12469, 12478, 13336, 13348, 13468, 13579 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Reinhard Zumkeller, First 10000 products of any two terms of A237424

EXAMPLE

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

.  n | a(n) = A237424(i) * A237424(j)

. ---+-------------------------------

.  1 |    1 = 1 * 1   = A237424(1)^2

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

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

.  4 |   16 = 4 * 4   = A237424(2)^2

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

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

.  7 {   37 = 4 * 37  = A237424(1) * A237424(5)

.  8 |   49 = 7 * 7   = A237424(3)^2

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

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

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

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

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

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

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

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

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

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

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

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

see link for more.

PROG

(Haskell)

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

import qualified Data.Set as Set (null)

a254143 n = a254143_list !! (n-1)

a254143_list = f a237424_list [] empty where

   f xs'@(x:xs) zs s

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

     | otherwise           = y : f xs' zs s'

     where zs' = x : zs

           (y, s') = deleteFindMin s

(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++)

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

CROSSREFS

Subsequence of A009994.

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

Sequence in context: A164123 A005513 A254323 * A025619 A093210 A133600

Adjacent sequences:  A254140 A254141 A254142 * A254144 A254145 A254146

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 28 2015

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)