Digitconsistent

Digitconsistent is a term used in mathematics and computer science to describe a property of numerical strings where the digits obey a fixed rule that relates each digit to the preceding digits. The concept is used in discussions of number representations, data validation, and puzzle design.

Definition: Let x be a positive integer with decimal digits d1 d2 ... dn. The number is digitconsistent if there exists a function f such that for all i > 1, di = f(d1, ..., d_{i-1}) mod 10. A common simple instance is the sum rule: di = (d1 + ... + d_{i-1}) mod 10. Under this rule, the digits of a digitconsistent number form a deterministic sequence.

Examples: The sequence of digits starting with d1 = 2 yields d2 = 2, d3 = 4, d4 = 8, d5 = 6, producing 22486 as a digitconsistent number under the sum rule. Other rules may enforce monotonicity, parity alternation, or digitwise equalities.

Applications: In recreational mathematics, digitconsistency can define puzzle constraints or encoding schemes. In data validation, ideas related to digit consistency appear in check-digit algorithms that link successive digits to detect errors, improving error-detection capabilities.

See also: digit, check digit, numeral system, sequence constraint.