Tensplusunitsn

Tensplusunitsn is a simple digit-based function used in recreational mathematics and coding contexts. For any nonnegative integer n, tensplusunitsn(n) is defined as the sum of the tens digit and the units digit in decimal notation. Equivalently, if a(n) denotes tensplusunitsn(n), then a(n) = floor(n/10) mod 10 + n mod 10. When n has fewer than two digits, the missing tens digit is treated as 0.

Examples help illustrate the definition. n = 0 yields 0; n = 7 yields 7; n = 42 yields 4 + 2 = 6; n = 99 yields 9 + 9 = 18; n = 125 yields 2 + 5 = 7. These demonstrate that the function reflects only the last two digits of n.

Properties and notes. The value of a(n) depends only on the last two digits of n, so a(n + 100) = a(n) for all n. The range in base 10 is from 0 to 18. The function is periodic with period 100 and can be described piecewise by fixed tens and units digits. It generalizes to other bases B by replacing 10 with the base: a_B(n) = floor(n/B) mod B + n mod B, with range 0 to 2(B−1). In base 10 this recovers the original tens-plus-units interpretation.

Usage and relevance. Tensplusunitsn appears in number puzzles and encoding schemes that rely on simple digit operations. It provides a compact measure of the last two digits and can be used to generate periodic sequences, lightweight checksums, or as a component in more complex digital functions.

See also: digit sum, digital root, base representation, modular arithmetic, last two digits.

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