What is the next logical number in the sequence 9 98 897 7986 68975?

Answer 1

579864 is next.

Reverse the digits of the previous number and append the original last number less 1.

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Alternatively, the next number is 42 since the sequence is defined by:

U{n} = (-45577n⁵ + 718680n⁴ - 4205695n³ + 11376200n² - 14054268n + 6210840)/20

In fact *ANY* number can logically follow the given 5 numbers since it is possible to find a polynomial to calculate the terms which will give the given numbers for n=1, 2, 3, 4, 5 and the required number for n = 6.

eg U{n} = (10212n⁵ - 146175n⁴ + 801690n³ - 2073425n² + 2484854n - 1077120)/4 will give the required first 5 numbers AND U{6} = 579864 (as is the likely answer to the question, but U{7} = 2591403 not 4689753 as the "reverse digits..." rule above gives - that would require a polynomial of degree 6).