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A232328 A generalized Engel expansion of 1/Pi. 4
4, 3, 6, 12, 51, 146, 280, 482, 687, 3825, 5646, 30904, 120121, 1344923, 2340376, 4456271, 194324055, 219784933, 976224357, 11584437417, 26402463827, 34635051144, 85031207055, 95014277980, 257962314442 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
For a description of two kinds of generalized Engel expansion of a real number see A232327. Compare with A006283 and A014012.
LINKS
Eric Weisstein's World of Mathematics, Pierce Expansion
Wikipedia, Engel Expansion
FORMULA
Define the map g(x) by g(x) = -x*ceiling(-1/x) - 1 and let g^n(x) denote the n-th iterate of g, with the convention that g^0(x) = x. Then a(n) = |ceiling(1/g^n(-1/Pi))| for n >= 0.
Generalized Engel series expansion: 1/Pi = 1/4 + 1/(4*3) - 1/(4*3*6) - 1/(4*3*6*12) + 1/(4*3*6*12*51) + 1/(4*3*6*12*51*146) - - + +.
MAPLE
#Define the n-th iterate of the map f(x) = x/b*ceiling(b/x) - 1
map_iterate := proc(n, b, x) option remember;
if n = 0 then
x
else
-1 + 1/b*thisproc(n-1, b, x)*ceil(b/thisproc(n-1, b, x))
end if
end proc:
#Define the terms of the expansion of x to the base b
a := n -> ceil(evalf(b/map_iterate(n, b, x))):
Digits:= 500:
#Choose values for x and b
x := -1/Pi: b:= -1:
seq(abs(a(n)), n = 0..24);
CROSSREFS
Sequence in context: A215336 A328650 A343891 * A276229 A077955 A077978
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Nov 27 2013
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)