A365718 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365717(i) = A365717(j) for all i, j >= 0, where A365717(n) = A348717(A356867(1+n)).

1, 2, 2, 2, 3, 4, 5, 6, 3, 2, 7, 4, 3, 8, 9, 10, 11, 12, 4, 13, 14, 6, 15, 16, 17, 18, 6, 2, 19, 5, 5, 20, 21, 22, 23, 9, 3, 24, 12, 9, 25, 26, 27, 28, 29, 12, 30, 31, 11, 32, 33, 34, 35, 36, 4, 37, 14, 8, 38, 39, 40, 41, 42, 6, 43, 36, 16, 44, 45, 46, 47, 48, 29, 49, 50, 18, 51, 52, 53, 54, 11, 2, 55, 7, 7, 56

Offset: 0

Author

Antti Karttunen, Sep 17 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A365717.

For all i, j >= 0: a(i) = a(j) => A365720(i) = A365720(j).

In contrast to austere A103391, which is easily computed from n's binary expansion, the scatter plot here with its slender seaweed-like branchings suggests that this sequence is not just a simple derivation of base-3 expansion of n.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..59049

Crossrefs

Cf. A348717, A356867, A365720.

Cf. also A103391 (similar transformation applied to A005940) and A365715 (compare the scatter plot).

Programs

PARI

up_to = 59049; \\ = 3^10.
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; };
A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==vecsum(digits(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); };
v365718 = rgs_transform(apply(A348717,A356867list(1+up_to)));
A365718(n) = v365718[1+n];