A336159 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336158(i) = A336158(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A336158(n)], i.e., of the ordered pair [A046523(A005940(1+n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A000265, A005940, A046523, A278222, A336158.

Cf. also A003602, A286163, A286622, A291762, A324400, A336149, A336156, A336157, A336160, A336162.

Programs

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));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A336158(n) = A046523(A000265(n));
Aux336159(n) = [A278222(n), A336158(n)];
v336159 = rgs_transform(vector(up_to, n, Aux336159(n)));
A336159(n) = v336159[n];