OFFSET
0,2
COMMENTS
How many times does each prime number appear in this sequence?
Are there infinitely many solutions of the form
(k!-p(n)) = p(r_1)*...*p(r_i); r_i < n for all i?
FORMULA
a(n) = A048765(prime(n)) - prime(n). - R. J. Mathar, Aug 25 2010
EXAMPLE
a(1) = 2! - p(1) = 2 - 2 = 0;
a(2) = 3! - p(2) = 6 - 3 = 3;
a(3) = 3! - p(3) = 6 - 5 = 1;
a(4) = 4! - p(4) = 24 - 7 = 17;
a(5) = 4! - p(5) = 24 - 11 = 13;
a(6) = 4! - p(6) = 24 - 13 = 11;
a(7) = 4! - p(7) = 24 - 17 = 7;
a(8) = 4! - p(8) = 24 - 19 = 5;
a(9) = 4! - p(9) = 24 - 23 = 1;
a(10) = 5! - p(10) = 120 - 29 = 91;
etc.
MAPLE
A048765 := proc(n) for i from 1 do if i! >= n then return i! ; end if; end do: end proc:
seq(A151918(n), n=1..80) ; # R. J. Mathar, Aug 25 2010
MATHEMATICA
Module[{fs=Range[10]!, p}, Join[{0}, Flatten[Table[p=Prime[n]; Select[ fs, #>p&, 1]-p, {n, 2, 70}]]]] (* Harvey P. Dale, Oct 04 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Apr 06 2008
EXTENSIONS
More terms from R. J. Mathar, Aug 25 2010
STATUS
approved