A068456 - OEIS

%I #17 Sep 08 2022 08:45:05

%S 1,0,0,0,1,0,0,0,5,7,9,5,2,12,13,10,10,4,4,4,14,4,10,14,12,9,22,9,11,

%T 9,8,14,26,25,28,22,35,0,24,0,20,18,13,21,31,30,22,24,19,34,16,42,36,

%U 46,35,46,32,16,34,53,11,44,45,49,36,49,13,53,67,53,63,11,9,9,16,37,59,8

%N Factorial expansion of zeta(7) = Sum_{n>=1} a(n)/n!.

%H G. C. Greubel, <a href="/A068456/b068456.txt">Table of n, a(n) for n = 1..2500</a>

%t t = Zeta[7]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* _Amiram Eldar_, Nov 25 2018 *)

%t With[{b = Zeta[7]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)

%o (PARI) vector(30,n,if(n>1,t=t%1*n,t=zeta(7))\1) \\ _M. F. Hasler_, Nov 25 2018

%o (PARI) default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(7)), floor(n!*zeta(7)) - n*floor((n-1)!*zeta(7))), ", ")) \\ _G. C. Greubel_, Nov 26 2018

%o (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,7))] cat [Floor(Factorial(n)*Evaluate(L,7)) - n*Floor(Factorial((n-1))*Evaluate(L,7)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018

%o (Sage)

%o def A068456(n):

%o     if (n==1): return floor(zeta(7))

%o     else: return expand(floor(factorial(n)*zeta(7)) - n*floor(factorial(n-1)*zeta(7)))

%o [A068456(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018

%Y Cf. A007514.

%K nonn

%O 1,9

%A _Benoit Cloitre_, Mar 10 2002

%E Name edited and keywords cons,easy removed by _M. F. Hasler_, Nov 25 2018