A365720 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365719(i) = A365719(j) for all i, j >= 0, where A365719(n) = A046523(A356867(1+n)).

1, 2, 2, 2, 3, 4, 4, 5, 3, 2, 4, 4, 3, 6, 6, 6, 7, 6, 4, 6, 8, 5, 9, 9, 10, 11, 5, 2, 4, 4, 4, 6, 8, 8, 9, 6, 3, 6, 6, 6, 12, 12, 9, 13, 10, 6, 10, 12, 7, 14, 13, 14, 15, 9, 4, 8, 8, 6, 9, 12, 12, 13, 12, 5, 12, 9, 9, 16, 16, 13, 17, 14, 10, 14, 18, 11, 19, 17, 20, 21, 7, 2, 4, 4, 4, 6, 8, 8, 9, 6, 4, 8, 8, 6, 12, 12, 12

Offset

0,2

Comments

Restricted growth sequence transform of A365719.

For all i, j >= 0:

A365718(i) = A365718(j) => a(i) = a(j),

a(i) = a(j) => A365721(i) = A365721(j),

a(i) = a(j) => A365722(i) = A365722(j).

Links

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

Prog

(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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
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); };
v365720 = rgs_transform(apply(A046523, A356867list(1+up_to)));
A365720(n) = v365720[1+n];

Crossrefs

Cf. A046523, A356867, A365718, A365720 (rgs-transform), A365721, A365722.

Cf. also A286622.

Sequence in context: A036015 A130521 A369574 * A332251 A342249 A090619

Adjacent sequences: A365717 A365718 A365719 * A365721 A365722 A365723

Keyword

nonn,look

Author

Antti Karttunen, Sep 17 2023

Status

approved