A318831 Restricted growth sequence transform of A278222(A000010(n)).

1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 1, 1, 1, 2, 3, 1, 2, 3, 4, 1, 3, 2, 3, 2, 5, 1, 6, 1, 3, 1, 2, 2, 3, 3, 2, 1, 3, 2, 7, 3, 2, 4, 8, 1, 7, 3, 1, 2, 4, 3, 3, 2, 3, 5, 8, 1, 6, 6, 3, 1, 2, 3, 3, 1, 4, 2, 4, 2, 3, 3, 3, 3, 6, 2, 8, 1, 9, 3, 7, 2, 1, 7, 5, 3, 4, 2, 3, 4, 6, 8, 3, 1, 2, 7, 6, 3, 4, 1, 9, 2, 2

Offset: 1

Author

Antti Karttunen, Sep 04 2018

Keywords

• nonn

Comments

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary expansion of A000010(n).

For all i, j: a(i) = a(j) => A295660(i) = A295660(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. also A000010, A278222, A295660, A318835.

Compare also with the scatterplots of A286622, A304101 and A318832.

Programs

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
A278222(n) = A046523(A005940(1+n));
v318831 = rgs_transform(vector(up_to,n,A278222(eulerphi(n))));
A318831(n) = v318831[n];