A067117 - OEIS

%I #17 Dec 21 2015 12:55:19

%S 1,6,20,51,102,171,244,306,340,3402,30928,257737,1982597,14161414,

%T 94409428,590058925,3470934853,19282971406,101489323191,507446615959,

%U 2416412456951,10983692986143,47755186896276,198979945401152

%N a(n) = floor((concatenation of first n natural numbers)/ (n!)).

%H Harry J. Smith, <a href="/A067117/b067117.txt">Table of n, a(n) for n = 1..200</a>

%e a(5) = floor(123456/(6!)) = floor(123456/720) = 171.

%p x:= 0:

%p for n from 1 to 200 do

%p   x:= x*10^(1+ilog10(n))+n;

%p   A[n]:= floor(x/n!)

%p od:

%p seq(A[n],n=1..100); # _Robert Israel_, Dec 20 2015

%t Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[n]]]/n!],{n,30}] (* _Harvey P. Dale_, Aug 27 2014 *)

%o (PARI) digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } Concat(a, b)= { return(a*10^digitsIn(b) + b) } { c=0; s=0; for (n=1, 200, c=Concat(c, n); s+=n; write("b067117.txt", n, " ", floor(c/n!)) ) } \\ _Harry J. Smith_, May 25 2010

%o (PARI) a007908(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s);

%o a(n) = a007908(n) \ n!; \\ _Altug Alkan_, Dec 20 2015

%Y Cf. A007908, A067116.

%K easy,nonn,base

%O 1,2

%A _Amarnath Murthy_, Jan 08 2002