Repeating sequence

In mathematics the exact word is repdigit: a number composed of one digit repeated, in a given base, usually base ten unless stated otherwise. A repdigit made only of ones, 11 or 111 or 1111, is a repunit, and every repdigit is a repunit multiplied by its digit, so 444 is 111 x 4. All repdigits are palindromes, though most palindromes are not repdigits. The base matters too, since a repdigit in base ten need not be one in base two.

Angel-number writing uses the word more loosely. Three of a kind, 111 or 777, is the classic case, but the same label gets stretched to cover patterned sequences that are not repdigits at all, among them 1212, 1234 and 1010. The reading is usually that a digit's ordinary numerological character is amplified by repetition, and that a four-digit form carries more weight than a three-digit one.

The distinction worth keeping is between the arithmetic fact and the reading placed on it. That a number's digits match is a property of how we happen to write it in base ten. Write the same quantity in Roman numerals or in binary and the pattern usually disappears. Meaning arrives when a tradition assigns it, and different traditions assign different things to the same three digits.