A067117 a(n) = floor((concatenation of first n natural numbers)/ (n!)).
1, 6, 20, 51, 102, 171, 244, 306, 340, 3402, 30928, 257737, 1982597, 14161414, 94409428, 590058925, 3470934853, 19282971406, 101489323191, 507446615959, 2416412456951, 10983692986143, 47755186896276, 198979945401152
Offset: 1
Examples
a(5) = floor(123456/(6!)) = floor(123456/720) = 171.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..200
Programs
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Maple
x:= 0: for n from 1 to 200 do x:= x*10^(1+ilog10(n))+n; A[n]:= floor(x/n!) od: seq(A[n],n=1..100); # Robert Israel, Dec 20 2015
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Mathematica
Table[Floor[FromDigits[Flatten[IntegerDigits/@Range[n]]]/n!],{n,30}] (* Harvey P. Dale, Aug 27 2014 *) -
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 -
PARI
a007908(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); a(n) = a007908(n) \ n!; \\ Altug Alkan, Dec 20 2015
Comments