What is the missing term of the sequence?

[Rob_Gandy]

What is the missing number in the sequence?

0, 1, 6, 105, 27 030,_______________, 7 608 434 000 728 254 870

The sequence

here may seem

unusual, but

examination

may reveal

obvious steps

required to

solve for each

element in it.

The method to find each term is actually pretty 'basic.'

Edited September 7, 2012 by Rob_Gandy

[Rainman]

We are building a binary string, starting with 0. We get the next string by switching all zeros and ones, then adding the switched string at the end of the original string.

0 (switch zeros and ones to get 1, add this at the end of the string to get the next number)

01 (switch zeros and ones to get 10, add this at the end to get...)

0110 (switch to get 1001, add to get...)

01101001 (switch to get 10010110, add to get...)

0110100110010110 (switch to get 1001011001101001, add to get...)

01101001100101101001011001101001 (this is the missing string, bring it back to decimal base to get 1,771,476,589)

[bonanova]

We are building a binary string, starting with 0. We get the next string by switching all zeros and ones, then adding the switched string at the end of the original string.

0 (switch zeros and ones to get 1, add this at the end of the string to get the next number)

01 (switch zeros and ones to get 10, add this at the end to get...)

0110 (switch to get 1001, add to get...)

01101001 (switch to get 10010110, add to get...)

0110100110010110 (switch to get 1001011001101001, add to get...)

01101001100101101001011001101001 (this is the missing string, bring it back to decimal base to get 1,771,476,589)

Impressive. Good puzzle, great solve!