A324390 Lexicographically earliest positive sequence such that a(i) = a(j) => A278219(i) = A278219(j) and A324386(i) = A324386(j), for all i, j >= 0.

1, 2, 3, 2, 3, 4, 5, 2, 6, 7, 8, 4, 5, 9, 10, 2, 3, 7, 11, 7, 8, 12, 13, 4, 14, 15, 16, 9, 17, 18, 14, 2, 6, 7, 19, 20, 11, 21, 22, 7, 23, 24, 25, 26, 27, 28, 27, 4, 14, 29, 30, 15, 31, 32, 33, 9, 34, 35, 36, 9, 37, 38, 37, 2, 39, 40, 11, 7, 41, 42, 43, 40, 41, 44, 45, 46, 47, 48, 47, 7, 49, 50, 51, 24, 52, 53, 54, 55, 56, 57, 58, 42, 59, 60, 56, 4, 61, 62, 63

Offset: 0

Author

Antti Karttunen, Feb 27 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A278219(n), A324386(n)].

Links

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

Crossrefs

Cf. A278219, A324386.

Cf. also A286619, A324343, A324344, A324380 (compare the scatter-plots).

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
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));
A003188(n) = bitxor(n, n>>1);
A278219(n) = A278222(A003188(n));
Aux324390(n) = [A278219(n), A324386(n)]; \\ See code for A324386 in that entry.
v324390 = rgs_transform(vector(1+up_to,n,Aux324390(n-1)));
A324390(n) = v324390[1+n];

Formula

a(A000225(n)) = 2 for all n >= 1.