OFFSET
1,3
COMMENTS
Number of 0's immediately following the decimal point in the expansion of (3-sqrt(8))^n.
LINKS
Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier, Convergence Acceleration of Alternating Series, Experiment. Math. Volume 9, Issue 1 (2000), 3-12, Project Euclid - Cornell Univ (see Proposition 1).
Robbert Fokkink, The Pell Tower and Ostronometry, arXiv:2309.01644 [math.CO], 2023.
Math Forum, Triangular Numbers That are Perfect Squares
Math Pages, On m = sqrt(sqrt(n) + sqrt(kn+1)) [Wrong link]
Robert Simms, Using counting numbers to generate Pythagorean triples
FORMULA
Roughly, floor(3*n/4)
EXAMPLE
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.
MATHEMATICA
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}] (* Robert G. Wilson v, Apr 10 2004 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marvin Ray Burns, Apr 10 2004
STATUS
approved