A304101 Restricted growth sequence transform of A278222(A048679(n)).

1, 2, 2, 2, 3, 2, 4, 3, 2, 4, 4, 3, 5, 2, 4, 4, 4, 6, 3, 6, 5, 2, 4, 4, 4, 6, 4, 7, 6, 3, 6, 6, 5, 8, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 3, 6, 6, 6, 10, 5, 9, 8, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 4, 7, 7, 7, 11, 6, 11, 9, 3, 6, 6, 6, 10, 6, 11, 10, 5, 9, 9, 8, 12, 2, 4, 4, 4, 6, 4, 7, 6, 4, 7, 7, 6, 9, 4, 7, 7, 7

Offset: 0

Author

Antti Karttunen, May 13 2018

Keywords

• nonn
• look

Comments

Positions of 2's is given by the positive Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, ..., that is, A000045(n) from n >= 2 onward.

Positions of 3's is given by Lucas numbers larger than 3: 4, 7, 11, 18, ..., that is, A000032(n) from n >= 3 onward.

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A048679(n). Compare to the scatter plot of A286622.

Links

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

Crossrefs

Cf. A000032, A000045, A003603, A007895, A035513, A048679, A278222, A304100, A304102, A304103, A304104, A304105.

Cf. also A286622 (compare the scatter-plots).

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; };
A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A003714(n) = { my(s=0,w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }
A106151(n) = if(n<=1, n, if(n%2, 1+(2*A106151((n-1)/2)), A106151(n>>valuation(n, 2))<<(valuation(n, 2)-1)));
A048679(n) = if(!n,n,A106151(2*A003714(n)));
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));
v304101 = rgs_transform(vector(1+up_to, n, A278222(A048679(n-1))));
A304101(n) = v304101[1+n];