A304745 Restricted growth sequence transform of A046523(A207901(n)).

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

Offset: 0

Author

Antti Karttunen, May 27 2018

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A005811(i) = A005811(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. A046523, A207901.

Cf. also A286619 (A278219), A304744.

Programs

PARI

up_to_e = 17; \\ Good for computing up to n = (2^up_to_e)-1
v050376 = vector(up_to_e);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e,break));
A050376(n) = v050376[n];
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A003188(n) = bitxor(n, n>>1);
A207901(n) = A052330(A003188(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
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; };
v304745 = rgs_transform(vector(65538,n,A046523(A207901(n-1))));
A304745(n) = v304745[1+n];