A367314 a(0) = 1; for n > 0, a(n) = lcm(a(n-1), a(n-2)+1, a(n-3)+2, ..., a(0)+n-1).

1, 1, 2, 6, 12, 420, 10920, 13791960, 31781240978760, 2475081972959523523910954640, 3442004402022863055515137969749021701676249608093520, 45446117889526225044218072480163823127876682090382722344419488836545177458721523373548206735891390800

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = lcm_{k=0..n-1} a(n-1 - k) + k with a(0)=1.

Example

                                        Prepend a(n-1)
                                 after incrementing the value
                                   in each of these columns
                                             | | | |
                                             v v v v
n=0:                                                     1 = a(0),
n=1: lcm(                      a(0)  ) = lcm(      1) =  1 = a(1),
n=2: lcm(              a(1),   a(0)+1) = lcm(    1,2) =  2 = a(2),
n=3: lcm(      a(2),   a(1)+1, a(0)+2) = lcm(  2,2,3) =  6 = a(3),
n=4: lcm(a(3), a(2)+1, a(1)+2, a(0)+3) = lcm(6,3,3,4) = 12 = a(4).

Prog

(Python)
import math
def a(n):
    p=[1]
    for i in range(n):
        p.append(math.lcm(*p))
        for x in range(0, len(p)-1):
            p[x]+=1
    return p[-1]

Crossrefs

Sequence in context: A291062 A058046 A298410 * A328448 A074180 A126293

Adjacent sequences: A367311 A367312 A367313 * A367315 A367316 A367317

Keyword

nonn

Author

Justin Dugan, Nov 13 2023

Status

approved