A275698 a(0) = 2, after that a(n) is 3 plus the least common multiple of previous terms.

2, 5, 13, 133, 17293, 298995973, 89398590973228813, 7992108067998667938125889533702533, 63873791370569400659097694858350356285036046451665934814399129508493

Offset: 0

Author

Andres Cicuttin, Aug 05 2016

Keywords

• nonn

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]

Crossrefs

Cf. A000058, A000215, A000289, A000324, A001543, A001544, A082732, A275664.

Programs

Mathematica

A275698 = {2}; Do[AppendTo[A275698, 3 + LCM@@A275698], {i, 9}]; A275698

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).