A009949 Factorial expansion of sqrt(2) = Sum_{n>=1} a(n)/n!, using greedy algorithm.
1, 0, 2, 1, 4, 4, 1, 5, 0, 8, 1, 11, 1, 7, 8, 4, 4, 4, 11, 13, 1, 6, 15, 13, 8, 12, 22, 25, 14, 9, 13, 11, 30, 9, 16, 25, 3, 12, 11, 2, 35, 41, 29, 29, 11, 27, 43, 32, 1, 16, 2, 5, 29, 3, 2, 30, 18, 30, 32, 56, 44, 38, 44, 27, 4
Offset: 1
Keywords
Examples
sqrt(2) = 1 + 0/2! + 2/3! + 1/4! + 4/5! + 4/6! + 1/7! + 5/8! + ...
Links
Crossrefs
Programs
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Magma
SetDefaultRealField(RealField(250)); [Floor(Sqrt(2))] cat [Floor(Factorial(n)*Sqrt(2)) - n*Floor(Factorial((n-1))*Sqrt(2)) : n in [2..80]]; // G. C. Greubel, Dec 10 2018
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Maple
A009949 := proc(a,n) local i,b,c; b := a; c := [ floor(b) ]; for i from 1 to n-1 do b := b-c[ i ]/i!; c := [ op(c), floor(b*(i+1)!) ]; od; c; end:
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Mathematica
With[{b = Sqrt[2]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Dec 10 2018 *) -
PARI
default(realprecision, 250); b = sqrt(2); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Dec 10 2018
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PARI
default(realprecision,900); my(t=sqrt(2)); for(n=1,80,t=t*n;print1(floor(t),", ");t=frac(t)); \\ Joerg Arndt, Dec 17 2018
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Sage
b=sqrt(2); def a(n): if (n==1): return floor(b) else: return expand(floor(factorial(n)*b) - n*floor(factorial(n-1)*b)) [a(n) for n in (1..80)] # G. C. Greubel, Dec 10 2018