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The formula may use any combination of the four binary operators +, -, *, /, the unary minus and parentheses. All digits have to be used exactly once and in the given order. Concatenation of the digits is not allowed. 0/0 in the evaluation of expressions makes the result invalid.

The last term a(7)=8985898, which is the only string of 7 digits for which it is not possible to construct an expression with result 0, is conjectured to be the last sequence term, i.e. for all strings of 8 or more digits expressions with result 0 can be found.

The conjecture is almost trivially true. Since 8985898 is the only exception for strings of 7 digits, an 8 digit string containing 8985898 can only be of the form x8985898 or 8985898x. But since any of x898589 and 985898x /= 8985898 leads to a 7 digit string that can represent 0, one can always find a substring of length 7 representing 0 in a string of 8 or more digits. Therefore the sequence ends at a(7).

For definitions and comments see A288350.

It is conjectured that a(n)=0 for n>=8.

The conjecture is true, as shown in the corresponding comment in A288350. - Hugo Pfoertner, Jun 09 2017

For definitions and comments see A288350. The b-file provides all A288351(4)=1500 sequence terms.

For definitions and comments see A288350. The b-file provides all A288351(5)=1014 sequence terms.

For definitions and comments see A288350. The b-file provides all A288351(6)=89 sequence terms.