A335421 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335422(i)) = A046523(A335422(j)) for all i, j >= 0.

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

Offset

0,4

Comments

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A335420(i) = A335420(j).

Links

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

Index entries for sequences related to binary expansion of n

Formula

For all n >= 0, a(2^n) = 1.

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; };
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
A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A163511(n) = if(!n, 1, A005940(1+A054429(n)))
A335422(n) = A005940(1+A163511(n));
v335421 = rgs_transform(vector(1+up_to, n, A046523(A335422(n-1))));
A335421(n) = v335421[1+n];

Crossrefs

Cf. A046523, A335420, A335422.

Cf. also A286622, A324400.

Sequence in context: A347205 A336161 A336160 * A263017 A245328 A060162

Adjacent sequences: A335418 A335419 A335420 * A335422 A335423 A335424

Keyword

nonn,look

Author

Antti Karttunen, Jun 09 2020

Status

approved