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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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...
متن کاملSequences of Generalized Happy Numbers with Small Bases
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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In this paper, we introduce and study the concepts of $mathcal{I}_2$-convergence, $mathcal{I}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{I}_2$ denotes the ideal of subsets of $mathbb N times mathbb N$. Also, we study some properties and relations of them.
متن کاملOn the Density of Happy Numbers
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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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2007
ISSN: 0035-7596
DOI: 10.1216/rmjm/1199649829