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In mathematical terms there is no "wrong" because no rule for generating the sequence has been defined. I can create seven different rules under which one of the given numbers is "wrong".

For example, if t(n) = (n5 - 23n4 + 203n3 - 847n2 + 1698n - 1244)/4 then the first number, 7, is "wrong".

But if t(n) = (n5 - 22n4 + 182n3 - 683n2 + 1170n - 606)/6 then the second number, 13, is "wrong".

It is easy enough to extend this list to the remaining five numbers so that each is "wrong" in the context of one rule or another.

By the above process,

if t(n) = (3n2 + 3n + 8)/2 then the fourth number, 31 is "wrong".

It could be argued that the generating rule is of the polynomial of the lowest order for 31, but that is hardly a good mathematical reason.

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13y ago

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