A365394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365426(i) = A365426(j) for all i, j >= 0.

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

Offset

0,4

Comments

Restricted growth sequence transform of the ordered pair [A365425(n), A365426(n)].

Restricted growth sequence transform of the function f(n) = A336470(A163511(n)).

For all i, j: a(i) = a(j) => A334204(i) = A334204(j).

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

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));
A365425(n) = A046523(A000265(A163511(n)));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365426(n) = A336466(A163511(n));
A365394aux(n) = [A365425(n), A365426(n)];
v365394 = rgs_transform(vector(1+up_to, n, A365394aux(n-1)));
A365394(n) = v365394[1+n];

Crossrefs

Cf. A000265, A003602, A046523, A163511, A336470, A365425, A365426.

Cf. also A350067, A365395, A366792 (compare the scatter plots).

Sequence in context: A336391 A366798 A366797 * A365391 A336390 A124758

Adjacent sequences: A365391 A365392 A365393 * A365395 A365396 A365397

Keyword

nonn,look

Author

Antti Karttunen, Sep 04 2023

Status

approved