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A287219 The numbers which are of the form (a*100 + b*10 + c)*(d*10 + e) = (f*10 + g)*(h*10 + i) (a, b, ... , i are nine digits, 1, 2, ... , 9). 0
3634, 3726, 3886, 4002, 4234, 4662, 5022, 5056, 5568, 7008, 7448 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Dudeney asked the largest number in 1917 and 7448 (= 532 * 14 = 98 * 76) was found in 1971.

REFERENCES

Henry Ernest Dudeney, Amusements in Mathematics, 1917.

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

Dudeney gave the following example.

158 * 23 = 79 * 46 (= 3634),

158 * 32 = 79 * 64 (= 5056),

174 * 32 = 96 * 58 (= 5568).

MATHEMATICA

Reap[Do[{a, b, c, d, e, f, g, h, i} = p; m = (a*100 + b*10 + c)*(d*10 + e); If[m == (f*10 + g)*(h*10 + i), Print[m]; Sow[m]], {p, Permutations[ Range[9]]}]][[2, 1]] // Union (* Jean-Fran├žois Alcover, May 22 2017 *)

PROG

(Ruby)

ary = []

(1..9).to_a.permutation{|a|

  i = a[0] * 100 + a[1] * 10 + a[2]

  j = a[3] * 10 + a[4]

  k = a[5] * 10 + a[6]

  l = a[7] * 10 + a[8]

  ary << i * j if i * j == k * l

}

p ary.uniq.sort

CROSSREFS

Sequence in context: A223414 A046835 A143930 * A232120 A232418 A206844

Adjacent sequences:  A287216 A287217 A287218 * A287220 A287221 A287222

KEYWORD

nonn,base,fini,full

AUTHOR

Seiichi Manyama, May 22 2017

STATUS

approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)