World!OfNumbers |
WON plate 167 | |
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The first edition of this book appeared in February, 2004 [ article by yours truly PDG ] Last month I received a copy by the author himself. He noticed ** The first topic Scintillating equations - Table (pp. 120) These are also known as pandigital Vampire Numbers and all vampire numbers are also Friedman Numbers - thx Bruno Curfs. The computer rendered 1289 solutions... a 'prime' total ! The smallest factor from the output list happens with You will surely like this nice pandigital with a _unique_ solution
The largest 5-digit factor is also the right substring of the pandigital itself ! Two factors occur each four times nl. 69135 and 98640 !
** Nine pandigitals can be factorized into
1239756840 = 18495 * 67032
1479635280 = 15864 * 93270
1954283760 = 37620 * 51948
2483619750 = 26475 * 93810
4031985672 = 49137 * 82056
4293156780 = 49260 * 87153 ** I did a likewise investigation but with The smallest such ninedigital is The smallest 4-digit factor happens with We notice that 5-digit number 98754 is the largest factor Here also two factors occur each four times
Now the reader is invited to multiply together 6351 * 9864 = 6264_6264 An eyecatching Parallel to episode 33 I compiled four ninedigital numbers
147963528 = 7932 * 18654
195428376 = 3762 * 51948
248361975 = 3975 * 62481
429315678 = 4926 * 87153 Note that the first one is very beautiful since the 4-digit 7932 * 18654 ** Episode 32 : Heptads (p. 19) is a spin-off of the above searching for digit 0 ( # 16 ) digit 1 ( # 11 ) digit 2 ( # 24 ) digit 3 ( # 17 ) digit 4 ( # 21 ) digit 5 ( # 10 ) digit 6 ( # 7 ) digit 7 ( # 2 ) digit 8 ( # 5 ) digit 9 ( # 0 ) A _twofold_ solution pops up if we keep the seven identical
56738 * 92041 Two 10-digits contain more than seven identical digits
Restricting the remaining digits to be identical leads us
The third solution again reveals to us the presence of The extended versions of the Beast are available as well !
To conclude this expansion on the subject two equations
The palindrome 62226 will come back in another format, ** Inspired by B.S. Rangaswamy's book I set out to look for 141 solutions came up which is a palindromic total ! The smallest one is 315867942 = 15486 * 20397 The largest one is 987561234 = 28179 * 35046 The uniqueness of the following result is that
The Beast took refuge in one of the 141 solutions !
** Episode 55 : Six Soldiers (p. 77) Particularly beautiful is this item because it Some not continuous solutions with only two distinct digits Also special is this item because the digits of the ** Awesome x anagrammatical x equations The first construct is with multiplicand 27489 and his
A second construct produces a ninedigital and a pandigital with
Finally three _still interesting_ leftovers from my search.
** Palindromes as products of two 5-digit factors. There are only ten palindromes consisting of nine digits
One anagrammatical combination shows up here.
Palindromes as products of a 4-digit and a 5-digit factor. There are three palindromes consisting of eight digits and
Five
One
** Mixed anagram equations starting from a common factor. The first and the last two constructions are remarkable in the Many examples I found are displayed as well but without
** Palindromic lookalikes. Behold the next two palindromes and get enchanted.
Compare the next two palindromes and get enchanted.
There exist imho no better constructions that can ** Scintillating equations with two 5-digit factors and their Below is shown an exceptionally nice pair of equations.
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A000167 Prime Curios! Prime Puzzle Wikipedia 167 Le nombre 167 |

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