A383284 Lexicographically earliest infinite sequence such that a(i) = a(j) => A265576(i) = A265576(j), for all i, j >= 1, where A265576 is the LCM-transform of EKG-sequence.

1, 2, 2, 3, 1, 3, 1, 2, 4, 1, 1, 1, 5, 1, 1, 1, 2, 1, 6, 1, 1, 3, 1, 4, 1, 1, 7, 1, 1, 1, 2, 8, 1, 1, 1, 9, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 12, 1, 1, 1, 2, 1, 13, 1, 1, 1, 1, 1, 1, 14, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17

Offset: 1

Author

Antti Karttunen, Apr 22 2025

Keywords

• nonn

Comments

Restricted growth sequence transform of A265576.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to EKG sequence.

Crossrefs

Cf. A000720, A064413, A265576, A383285 (positions of terms > 1).

Positions of records: {2} U A064423.

Programs

PARI

up_to = 100000;
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); };
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
v064413 = readvec("b064413_huge_to.txt"); \\ From b-file of A064413 computed previously.
A064413(n) = v064413[n];
v383284 = rgs_transform(LCMtransform(vector(up_to, i, A064413(i))));
A383284(n) = v383284[n];

Formula

a(n) = 1+A000720(A265576(n)). [Conjectured. True if there are no composites in A265576]