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A009949 Factorial expansion of sqrt(2) = Sum_{n>=1} a(n)/n!, using greedy algorithm. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for factorial base representation

EXAMPLE

sqrt(2) = 1 + 0/2! + 2/3! + 1/4! + 4/5! + 4/6! + 1/7! + 5/8! + ...

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:

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 *)

PROG

(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

(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

(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

(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

CROSSREFS

Cf. A002193 (decimal expansion), A040000 (continued fraction).

Cf. A067881 (sqrt(3)), A068446 (sqrt(5)), A320839 (sqrt(7)).

Sequence in context: A274826 A129862 A137593 * A070785 A214985 A105537

Adjacent sequences:  A009946 A009947 A009948 * A009950 A009951 A009952

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Bill Gosper

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)