منابع مشابه
On Consecutive Happy Numbers
Let e > 1 and b > 2 be integers. For a positive integer n = ∑k j=0 aj × b j with 0 6 aj < b, define
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The happy function H : N → N sends a positive integer to the sum of the squares of its digits. A number x is said to be happy if the sequence {Hn(x)}∞ n=1 eventually reaches 1 (here H(x) denotes the nth iteration of H on x). A basic open question regarding happy numbers is what bounds on the density can be proved. This paper uses probabilistic methods to reduce this problem to experimentally fi...
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For bases b ≤ 5 and exponents e ≥ 2, there exist arbitrarily long finite sequences of d-consecutive e-power b-happy numbers for a specific d = d(e, b), which is shown to be minimal possible.
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A happy number N is defined by the condition S(N ) = 1 for some number n of iterations of the function S, where S(N ) is the sum of the squares of the digits of N . Up to 10, the longest known string of consecutive happy numbers was length five. We find the smallest string of consecutive happy numbers of length 6, 7, 8, . . . , 13. For instance, the smallest string of six consecutive happy numb...
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We compare our own embodied conversational agent (ECA) scheme, BotCom, with seven other complex Internet-based ECAs according to recentlypublished information about them, and highlight some important attributes that have received little attention in the construction of realistic ECAs. BotCom incorporates the use of emotions, humor and complex information services. We cover issues that are likel...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2000
ISSN: 0035-7596
DOI: 10.1216/rmjm/1022009281