A365391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j) and A365425(i) = A365425(j) for all i, j >= 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 5, 2, 6, 1, 7, 4, 8, 3, 9, 3, 3, 2, 10, 5, 11, 2, 5, 6, 2, 1, 12, 7, 13, 4, 14, 8, 15, 3, 16, 9, 17, 3, 18, 3, 3, 2, 19, 10, 9, 5, 20, 11, 21, 2, 9, 5, 5, 6, 5, 2, 22, 1, 23, 12, 24, 7, 25, 13, 7, 4, 26, 14, 27, 8, 28, 15, 8, 3, 29, 16, 16, 9, 30, 17, 9, 3, 16, 18, 9, 3, 9, 3, 31, 2

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A336158(n), A365425(n)].

For all i, j:

A003602(i) = A003602(j) => a(i) = a(j),

A365392(i) = A365392(j) => a(i) = a(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(PARI)
up_to = 65537;
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; };
A000265(n) = (n>>valuation(n, 2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365391aux(n) = [A046523(A000265(n)), A046523(A000265(A163511(n)))];
v365391 = rgs_transform(vector(up_to, n, A365391aux(n)));
A365391(n) = v365391[n];

Crossrefs

Cf. A000265, A003602, A046523, A163511, A336158, A365425, A365392.

Cf. also A286531, A336159.

Sequence in context: A366798 A366797 A365394 * A336390 A124758 A198328

Adjacent sequences: A365388 A365389 A365390 * A365392 A365393 A365394

Keyword

nonn,look

Author

Antti Karttunen, Sep 03 2023

Status

approved