OFFSET
0,1
COMMENTS
This sequence could be considered a particular case of a possible two-parameter family of sequences of the form: a(n) = k1 + lcm(a(0),a(1),..,a(n-1)), a(0) = k2, where in this case k1=3 and k2=2. With other choices of k1 and k2 it seems it is possible to generate other sequences such as
A129871 with k1 = 1 and k2 = 1,
A000058 with k1 = 1 and k2 = 2,
A082732 with k1 = 1 and k2 = 3,
A000215 with k1 = 2 and k2 = 3,
A000324 with k1 = 4 and k2 = 1,
A001543 with k1 = 5 and k2 = 1,
A001544 with k1 = 6 and k2 = 1,
A275664 with k1 = 2 and k2 = 2,
A000289 with k1 = 3 and k2 = 1.
LINKS
S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
S. Mustonen, On integer sequences with mutual k-residues
Seppo Mustonen, On integer sequences with mutual k-residues [Local copy]
FORMULA
a(n) = 3 + lcm(a(0), a(1), ..., a(n - 1)), a(0) = 2.
a(n) = 3 + a(n-1)*(a(n-1)-3), for n > 1. - Christian Krause, Oct 17 2023. Proof: Follows from associativity of lcm(...) and the fact that gcd(m,m+3)=1:
a(n)-3 = lcm(a(0),a(1),...,a(n-2),a(n-1))
= lcm(lcm(a(0),a(1),...,a(n-2)),a(n-1))
= lcm(a(n-1)-3,a(n-1))
= (a(n-1)-3)*a(n-1).
CROSSREFS
KEYWORD
nonn
AUTHOR
Andres Cicuttin, Aug 05 2016
STATUS
approved