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).

3634, 3726, 3886, 4002, 4234, 4662, 5022, 5056, 5568, 7008, 7448

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-François 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: A046835 A143930 A341264 * A232120 A232418 A206844

Adjacent sequences: A287216 A287217 A287218 * A287220 A287221 A287222

Keyword

nonn,base,fini,full

Author

Seiichi Manyama, May 22 2017

Status

approved