A324345 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A278222(i) = A278222(j), for all i, j >= 0.

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

Offset: 0

Author

Antti Karttunen, Feb 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A005811(n), A278222(n)], or equally, of [A005811(n), A286622(n)].

For all i, j >= 1:

a(i) = a(j) => A033264(i) = A033264(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005811, A278222, A286622.

Cf. also A033264, A323889, A324343, A324346.

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; };
A005811(n) = hammingweight(bitxor(n, n>>1)); \\ From A005811
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));
Aux324345(n) = [A005811(n), A278222(n)];
v324345 = rgs_transform(vector(1+up_to,n,Aux324345(n-1)));
A324345(n) = v324345[1+n];

Formula

a(2^n) = 3 for all n >= 1.