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The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest number of multiplicative persistence 3.
The next number in the sequence (the smallest number of additive persistence 5) is 2 × 10 2×(10 22 − 1)/9 − 1 (that is, 1 followed by 2 222 222 222 222 222 222 222 nines). For any fixed base, the sum of the digits of a number is proportional to its logarithm ; therefore, the additive persistence is proportional to the iterated logarithm .
Based on these restrictions, the number of candidates for -digit numbers with record-breaking persistence is only proportional to the square of , a tiny fraction of all possible -digit numbers. However, any number that is missing from the sequence above would have multiplicative persistence > 11; such numbers are believed not to exist, and ...
The article uses the terms daughter and parent to describe composites and the primes that they lead to, with numbers leading to the same home prime called siblings (even if one is an iterate of another), and calls the number of iterations required to reach a parent, the persistence of a number under the map to obtain a home prime, the number of ...
Image persistence, in LCD monitors; Persistence (computer science), the characteristic of data that outlives the execution of the program that created it; Persistence of a number, a mathematical quality of numbers; Persistent data structure, a data structure that always preserves the previous version of itself when it is modified
The iterated logarithm is closely related to the generalized logarithm function used in symmetric level-index arithmetic.The additive persistence of a number, the number of times someone must replace the number by the sum of its digits before reaching its digital root, is ().
Time and again, however, scientists have crunched the numbers and determined that the 27 Club has more basis in myth than in math. Read more: Taylor Swift's new album is rife with breakup songs ...
By the way, I don't think the term persistence of a number is used in mathematics for anything but the additive and multiplicative persistence. Therefore, I think we can get rid of the overly abstract first sentence and just say what additive and multiplicative persistence is.