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Search: id:A093700
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| A093700 |
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Number of 9's immediately following the decimal point in the expansion of (3+sqrt(8))^n. |
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+0
1
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| 0, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 48, 49, 50, 51, 52, 52, 53, 54, 55, 55, 56, 57
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Number of 0's immediately following the decimal point in the expansion of (3-sqrt(8))^n.
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LINKS
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Math Forum, Triangular Numbers That are Perfect Squares
Math Pages, On m = sqrt(sqrt(n) + sqrt(kn+1))
Project Euclid - Cornell Univ., Title? (see Proposition 1)
Robert Simms, Using counting numbers to generate Pythagorean triples
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FORMULA
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Roughly, floor(3*n/4)
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EXAMPLE
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Let n=10, (3+sqrt(8))^10= 45239073.9999999778... (the fractional part starts with seven 9's), so the 10th element in this sequence is 7.
The 132nd element is 100. The 1000th element is 765. The 1307th element is 1000.
The arrangement of repeating elements are like A074184 (Index of the smallest power of n >= n!) and A076539 (Numerators a(n) of fractions slowly converging to pi) and A080686 (Number of 19-smooth numbers <= n).
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MATHEMATICA
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For[n = 1, n < 999, n++, Block[{$MaxExtraPrecision = 50*n}, Print[ -Floor[Log[10, 1 - N[FractionalPart[(3 + 2Sqrt[2])^n], n]]] - 1]]]
f[n_] := Block[{}, -MantissaExponent[(3 - Sqrt[8])^n][[2]]]; Table[ f[n], {n, 75}] (from Robert G. Wilson v Apr 10 2004)
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CROSSREFS
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Cf. A003499, A050608, A080686, A076539, A074184.
Sequence in context: A057353 A076539 A074184 this_sequence A118168 A083920 A066508
Adjacent sequences: A093697 A093698 A093699 this_sequence A093701 A093702 A093703
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KEYWORD
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nonn,base
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AUTHOR
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Marvin Ray Burns (bmmmburns(AT)sbcglobal.net), Apr 10 2004
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