Abstract
A generalized happy function, maps a positive integer to the sum of its base digits raised to the -th power. We say that is a base-, -power, height-, -attracted number if is the smallest positive integer such that . Happy numbers are then base-10, 2-power, 1-attracted numbers of any height. Let denote the smallest height-, -attracted number for a fixed base and exponent and let denote the smallest number such that every integer can be written as for some nonnegative integers . We prove that if is the smallest nonnegative integer such that ,
and , then .
Citation
May Mei. Andrew Read-McFarland. "Numbers and the heights of their happiness." Involve 11 (2) 235 - 241, 2018. https://doi.org/10.2140/involve.2018.11.235
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