A322505 Factorial expansion of 1/sqrt(2) = Sum_{n>=1} a(n)/n!.

0, 1, 1, 0, 4, 5, 0, 6, 4, 9, 0, 11, 7, 3, 11, 10, 2, 2, 5, 16, 11, 3, 7, 18, 16, 19, 11, 12, 21, 19, 22, 5, 31, 21, 25, 30, 20, 6, 5, 21, 17, 41, 36, 14, 28, 13, 45, 16, 0, 33, 1, 2, 41, 1, 28, 43, 9, 15, 16, 28, 22, 19, 22, 13, 34, 61, 38, 40, 56, 44, 69, 25, 42, 44, 34, 73, 71, 42, 17

Offset: 1

Author

G. C. Greubel, Dec 12 2018

Keywords

• nonn

Examples

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

Links

• Index entries for factorial base representation

Crossrefs

Cf. A010503 (decimal expansion), A130130 (continued fraction).

Cf. A009949 (sqrt(2)).

Programs

Magma

SetDefaultRealField(RealField(250));  [Floor(1/Sqrt(2))] cat [Floor(Factorial(n)/Sqrt(2)) - n*Floor(Factorial((n-1))/Sqrt(2)) : n in [2..80]];

Mathematica

With[{b = 1/Sqrt[2]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Dec 12 2018 *)

PARI

default(realprecision, 250); b = 1/sqrt(2); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))

Sage

b=1/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)]