A102730 Number of factorials contained in the binary representation of n!
1, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 7, 8, 6, 7, 6, 7, 6, 7, 7, 7, 8, 7, 7, 7, 6, 8, 7, 7, 7, 7, 7, 8, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 8, 8, 7, 7, 7, 8, 8, 7, 8, 7, 7
Offset: 0
Examples
n = 6: 6! = 720 -> '1011010000' contains a(6) = 5 factorials: 0! = 1 -> '1', 1! = 1 -> '1', 2! = 2 -> '10', 3! = 6 -> '110' and 6! itself, but not 4! = 24-> '11000' and 5! = 120 -> '1111000'.
Links
Crossrefs
Programs
-
Mathematica
a[n_] := Sum[Boole[StringContainsQ[IntegerString[n!, 2], IntegerString[k!, 2]]], {k, 0, n}]; Array[a, 100, 0] (* Amiram Eldar, Apr 03 2025 *) -
PARI
contains(v,u)=for(i=0,#v-#u,for(j=1,#u,if(v[i+j]!=u[j],next(2)));return(1));0 a(n)=my(v=binary(n--!));sum(i=0,n-1,contains(v,binary(i!)))+1 \\ Charles R Greathouse IV, Aug 21 2011
Comments