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

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

Author

Pedja Terzic, May 19 2018

Keywords

• nonn

Comments

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

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

Links

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

Crossrefs

Cf. A135504, A217662, A217663, A304821.

Programs

Mathematica

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 *)

PARI

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)}

Python

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