For example, I have a sequence
Is there a word in the dictionary to represent
a sequence of repetitive/recurring digits
This type of number is commonly called a repdigit number, or sometimes a monodigit number. This term is used most frequently in recreational mathematics and is most often seen in investigations into prime numbers.
See wikipedia article on repdigit for details.
It's called a periodic sequence. See wikipedia.
The given example is not a sequence per se, considering that the "digits" are not separated (by a comma, space).
A natural number whose digits are repeating in some positional number system is called, in recreational mathematics, a repdigit. This comes from repeated and digit. In the case it is composed of digit 1 (1, 11, 111, 11111), it is called a repunit. The latter was coined by A. H. Beiler in 1966. See Repunit and Repdigit Numbers for other details.
Otherwise, this would just be a constant sequence:
Constant sequences are sequences for which all terms are the same.
• thefreedictionary.com defines repetend as “Mathematics The digit or group of digits that repeats infinitely in a repeating decimal”.
• collinsdictionary.com defines repetend as “(mathematics) the digit or series of digits in a recurring decimal that repeats itself”.
• Wiktionary defines repetend as “(mathematics) A repeating decimal”, which while closer to what you've asked about – ie the sequence of repeated numbers rather than the digits that repeat – is probably an incorrect definition.
The closest single word would be repetend, which generally means anything that is repeated (e.g. it would also be used about music and poetry).
Unfortunately, the one thing we cannot use it for is repeating numbers, because it has a specific sense when it comes to numbers where it only refers to the repeated numbers found in representing a fraction that cannot be fully represented in the base used (e.g. ⅓ in decimal ends with a repetend of 3, 1/7 in decimal has a repetend of 142857, ⅓ in binary ends with a repetend of 01, 1/10 in binary ends with a repetend of 0011, and so on).
So, while in that one case it is the perfect word to use, in any others it is a particularly bad word to use, because it will make people think of that more specific use.
In other cases I would just use "recurring sequence" or "repeated sequence".