A304738 Restricted growth sequence transform of A278222(A048673(n)).

1, 1, 2, 3, 1, 1, 2, 4, 5, 5, 4, 6, 3, 3, 3, 7, 3, 5, 2, 1, 4, 3, 8, 3, 5, 5, 9, 5, 1, 10, 5, 11, 3, 6, 6, 6, 7, 5, 10, 12, 5, 10, 2, 13, 5, 5, 14, 15, 11, 7, 2, 10, 8, 11, 6, 16, 6, 11, 17, 11, 3, 4, 7, 18, 8, 5, 3, 10, 7, 6, 7, 16, 3, 17, 19, 5, 3, 1, 7, 6, 20, 3, 10, 17, 5, 6, 6, 5, 5, 6, 11, 5, 20, 3, 7, 5, 14, 15, 10, 21, 5, 11, 14, 13, 5

Offset: 1

Author

Antti Karttunen, May 18 2018

Keywords

• nonn

Comments

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A048673(n). Compare to the scatter plot of A286622.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65539
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A048673, A278222, A286622.

Cf. also A286243, A304101, A304737.

Programs

PARI

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
A278222(n) = A046523(A005940(1+n));
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
v304738 = rgs_transform(vector(65539,n,A278222(A048673(n))));
A304738(n) = v304738[n];