Decimalof12

Decimalof12 is a fictional or informal mathematical construct used in recreational number theory and puzzle contexts to explore decimal constants formed by concatenating the decimal representations of a simple sequence. In the standard conception, one lists the powers of 12: 12^1, 12^2, 12^3, and so on, and writes their decimal representations successively without separators. The resulting infinite decimal, sometimes called the Decimalof12 constant, begins 0.121441728207362... and continues with 3072, 384, 4624, 559872, etc. Because the block lengths increase and the blocks themselves do not repeat in a regular pattern, the decimal expansion does not repeat and is therefore irrational.

Although not part of established mathematics as a formal object, Decimalof12 is used to illustrate properties of Champernowne-type constants, digit distribution heuristics, and questions about normality. Variants include concatenating powers of other bases or concatenating successive terms of other sequences, such as natural numbers, factorials, or Fibonacci numbers, producing a family of related constants often discussed in classrooms or online forums.

Origin and use: the term appears in puzzle collections and educational blogs as a simple, tangible example of constructing nontrivial decimals from sequences. It is not associated with proven theorems; rather, it serves as a didactic tool and curiosity for exploring how different concatenation schemes affect decimal structure.

See also: Champernowne constant, base-12 (duodecimal) system, normal number, decimal expansion, sequences and series.