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- W1966200050 abstract "Let e ⩾ 1 and b ⩾ 2 be integers. For a positive integer n = ∑ j = 0 k a j × b j with 0 ⩽ a j < b , define S e , b ( n ) = ∑ j = 0 k a j e . n is called ( e , b ) -happy if S e , b r ( n ) = 1 for some r ⩾ 0 , where S e , b r is the r th iteration of S e , b . In this paper, we prove that there exist arbitrarily long sequences of consecutive ( e , b ) -happy numbers provided that e − 1 is not divisible by p − 1 for any prime divisor p of b − 1 ." @default.
- W1966200050 created "2016-06-24" @default.
- W1966200050 creator A5067074347 @default.
- W1966200050 date "2008-06-01" @default.
- W1966200050 modified "2023-10-17" @default.
- W1966200050 title "On consecutive happy numbers" @default.
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- W1966200050 doi "https://doi.org/10.1016/j.jnt.2007.11.009" @default.
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