A079759 Let b(0)=0. For n >= 1, b(n) is the least k > b(n-1)+1 such that k divides (k-1)!/b(n-1)!, and a(n) = (b(n)-1)!/(b(n-1)!*b(n)).

1, 20, 4620, 12697776, 159845400, 941432800, 158800433792, 1895312483064000, 3438271897004237230080, 933561026438040, 2562849175892544, 640904462719404383808000, 1528364130975, 2352733350786, 959393282698730880000, 6142080926952

Offset: 1

Author

Amarnath Murthy, Jan 10 2003

Keywords

• nonn

Comments

Group the natural numbers so that every 2n-th group product is divisible by the single number in the next group. (1), (2,3,4,5), (6), (7,8,9,10,11), (12), (13,14,15,16,17,18,19),(20), (21,22,23,24,25,26,27),(28),...Sequence contains the ratio of the product of terms in 2n-th group and the (2n+1)-th group.

Examples

			a(1) = 1*2*3*4*5/6 = 20, a(2) = 7*8*9*10*11/12 = 4620, a(3) = 13*14*15*16*17*18*19/20 = 12697776, a(4) = 159845400 = 21*22*...*27/28.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10001 (corrected by Robert Israel, Jan 20 2019)

Crossrefs

Cf. A079759, A079760, A109895, A109896, A109897.

Programs

Maple

t:= 0:
for n from 1 to 30 do
  p:= t+1;
  for j from t+2 while not (p/j)::integer do p:= p*j od;
  A[n]:= p/j;
  t:= j;
od:
seq(A[i],i=1..30); # Robert Israel, Jul 16 2018

Mathematica

a[1] = 1; t = 0; nmax = 16; For[n = 1, n <= nmax, n++, p = t+1; For[j = t+2, Not[IntegerQ[p/j]], j++, p = p*j]; a[n+1] = p/j; t = j];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Mar 25 2019, after Robert Israel *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com) and Sascha Kurz, Jan 12 2003

Edited by N. J. A. Sloane, Nov 04 2018 at the suggestion of Georg Fischer. This entry now contains the merger of two identical sequences submitted by the same author.