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A277854
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Frequent terms, i.e., values such that no smaller value appears more often, in A075771 = quotient + remainder of Euclidean division of n^2 by prime(n).
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3
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1, 2, 4, 5, 9, 15, 16, 48, 64, 86, 100, 144, 169, 3364, 3969, 4096, 195364
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OFFSET
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1,2
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COMMENTS
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Equivalently, record values (in the weak sense of >=) in the sequence of frequencies of values of A075771. (The lower bound A075771(n) >= n^2/prime(n) ensures that no number below this limit can occur beyond the index n in that sequence.)
It appears that this sequence contains mainly squares, but there are exceptions such as 2, 5, 15, 48, 86, and some squares (25 = 5^2, 36 = 6^2, 49 = 7^2, 81 = 9^2, 121 = 11^2) do not occur. Is there an explanation for this and/or the fact that exceptions are close to missing squares: 48 ~ 49 = 7^2, 86 ~ 81 = 9^2 ? Can one prove or disprove that
- from some point on, only squares will occur?
- all sufficiently large squares (or: even squares?) will occur?
- from a(12) = 144 (or some later point) on, a(n) will occur in A075771 strictly more often than the preceding value?
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LINKS
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EXAMPLE
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Values that occur in A075771 not less often than any smaller value are 1, 2, 4 (which appear once), 5, 9, 15 (which appear twice), 16, 48, 64, 86, 100 (which appear three times), 144 (which appears five times), 169 (which appears seven times), ...
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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