A369060 LCM-transform of Sycamore's D(3) variant of Doudna sequence (A356867).

1, 2, 3, 5, 2, 1, 1, 2, 3, 7, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 2, 3, 11, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 3, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jan 13 2024

Keywords

• nonn

Comments

See discussion at A368900.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683

Crossrefs

Cf. A014963, A356867, A368900.

Programs

PARI

up_to = 3^9; \\ Checked up to (3^12)
A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==sumdigits(i,3), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };
v356867 = A356867list(up_to);
A356867(n) = v356867[n];
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2,len, g[n] = lcm(g[n-1],v[n]); b[n] = g[n]/g[n-1]); (b); };
v369060 = LCMtransform(v356867);
A369060(n) = v369060[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

Formula

a(n) = lcm {1..A356867(n)} / lcm {1..A356867(n-1)}.

a(n) = A014963(A356867(n)). [This holds because A356867 satisfies the property S explained in A368900]