A217663 -id:A217663 - cp's OEIS frontend

A217662 For n > 2 , a(n) = a(n-2) + lcm(a(n-2), n-1) with a(1)=2, a(2)=2.

2, 2, 4, 8, 8, 48, 32, 384, 64, 1536, 384, 18432, 768, 258048, 6144, 1548288, 12288, 27869184, 49152, 557383680, 294912, 1114767360, 3538944, 26754416640, 7077888, 160526499840, 99090432, 321052999680, 198180864, 9631589990400, 1189085184, 308210879692800

Offset: 1

Pedja Terzic, Oct 10 2012

nonn

A217663(n) = a(n+2)/a(n)-1 consists of 1's and primes only.

Cf. A135504.

RecurrenceTable[{a[n]==a[n-2]+LCM[n-1,a[n-2]],a[1] == 2,a[2]==2},a,{n,1, 24}]
t = {2, 2}; Do[AppendTo[t, t[[-2]] + LCM[n-1, t[[-2]]]], {n, 3, 40}]; t (* T. D. Noe, Oct 10 2012 *)
nxt[{n_,a_,b_}]:={n+1,b,a+LCM[a,n]}; NestList[nxt,{2,2,2},40][[All,2]] (* Harvey P. Dale, Aug 20 2020 *)

For prime p > 2, a(p+1) = (p+1)*a(p-1), which proves the statement in A217663. - M. F. Hasler, Oct 11 2012

A304822 a(n) = A304821(n+3)/A304821(n) - 1.

Original entry on oeis.org

1, 1, 2, 5, 1, 7, 1, 3, 5, 11, 1, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 1, 5, 13, 3, 1, 29, 5, 31, 1, 11, 17, 1, 1, 37, 19, 13, 1, 41, 1, 43, 11, 5, 23, 47, 1, 7, 1, 17, 13, 53, 1, 1, 1, 19, 29, 59, 1, 61, 31, 1, 1, 13, 11, 67, 17, 23, 1, 71, 1, 73

Offset: 1

Pedja Terzic, May 19 2018

nonn

Conjecture: This sequence consists of 1's and primes only.

a(n) divides n+1. - A.H.M. Smeets, Jul 02 2018

A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Cf. A135504, A217662, A217663, A304821.

Drop[#, 3] &@ Fold[Append[#1, {#2, #2/#1 - 1} & @@ {#1[[-3, 1]], #1[[-3, 1]] + LCM[#1[[-3, 1]], #2 + 1]}] &, {{6, 0}, {6, 0}, {6, 0}}, Range@ 72] [[All, -1]] (* Michael De Vlieger, May 20 2018 *)

Generator(n)={b1=6;b2=6;b3=6;list=[];for(k=4,n,b4=b1+lcm(k-2,b1);a=b4/b1-1;list=concat(list,a);b1=b2;b2=b3;b3=b4);print(list)}

from math import gcd
n,an0,an1,an2 = 3,6,6,6
while n-3 < 200:
    n += 1
    an0,an1,an2,an3 = an2+an2*(n-2)//gcd(an2,n-2),an0,an1,an2
    # an0 = A304821(n), an3 = A304821(n-3)
    print(n-3,an0//an3-1)
# A.H.M. Smeets, Jul 02 2018

cp's OEIS Frontend

A217662 For n > 2 , a(n) = a(n-2) + lcm(a(n-2), n-1) with a(1)=2, a(2)=2.

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