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

1,2

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.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A177323 A184891 A279297 * A109894 A227765 A250020

Adjacent sequences: A079756 A079757 A079758 * A079760 A079761 A079762

Keyword

nonn

Author

Amarnath Murthy, Jan 10 2003

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.

Status

approved