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A275698
a(0) = 2, after that a(n) is 3 plus the least common multiple of previous terms.
1
2, 5, 13, 133, 17293, 298995973, 89398590973228813, 7992108067998667938125889533702533, 63873791370569400659097694858350356285036046451665934814399129508493
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
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).
MATHEMATICA
A275698 = {2}; Do[AppendTo[A275698, 3 + LCM@@A275698], {i, 9}]; A275698
KEYWORD
nonn
AUTHOR
Andres Cicuttin, Aug 05 2016
STATUS
approved