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Search: id:A064896
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| A064896 |
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Numbers of the form (2^{mr}-1)/(2^r-1) for positive integers m, r. |
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+0
6
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| 1, 3, 5, 7, 9, 15, 17, 21, 31, 33, 63, 65, 73, 85, 127, 129, 255, 257, 273, 341, 511, 513, 585, 1023, 1025, 1057, 1365, 2047, 2049, 4095, 4097, 4161, 4369, 4681, 5461, 8191, 8193, 16383, 16385, 16513, 21845, 32767, 32769, 33825, 37449, 65535, 65537
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Binary expansion of n consists of single 1's diluted by (possibly empty) equal-sized blocks of 0's.
A064894(a(n)) = A056538(n)
According to Stolarsky's Theorem 2.1, all numbers in this sequence are sturdy numbers; this sequence is a subsequence of A125121. - T. D. Noe, Jul 21 2008
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REFERENCES
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T. Chinburg and M. Henriksen, Sums of k-th powers in the ring of polynomials with integer coefficients, Acta Arithmetica, 29 (1976), 227-250.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
K. B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica, 38 (1980), 117-128.
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EXAMPLE
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73 is included because it is 1001001 in binary, whose 1's are diluted by blocks of two 0's.
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MAPLE
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f := proc(p) local m, r, t1; t1 := {}; for m from 1 to 10 do for r from 1 to 10 do t1 := {op(t1), (p^(m*r)-1)/(p^r-1)}; od: od: sort(convert(t1, list)); end; f(2); # very crude!
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CROSSREFS
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A064894, A056538.
Adjacent sequences: A064893 A064894 A064895 this_sequence A064897 A064898 A064899
Sequence in context: A029608 A121820 A006995 this_sequence A076188 A073674 A083566
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KEYWORD
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base,easy,nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Oct 11 2001
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