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

1,3

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

Prog

(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];

Crossrefs

Cf. A003961, A048673, A278222, A286622.

Cf. also A286243, A304101, A304737.

Sequence in context: A152735 A249128 A299481 * A046226 A054722 A295260

Adjacent sequences: A304735 A304736 A304737 * A304739 A304740 A304741

Keyword

nonn

Author

Antti Karttunen, May 18 2018

Status

approved