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

1,7

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

Prog

(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];

Crossrefs

Cf. also A000010, A278222, A295660, A318835.

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

Sequence in context: A072347 A368684 A351034 * A303710 A263280 A136107

Adjacent sequences: A318828 A318829 A318830 * A318832 A318833 A318834

Keyword

nonn

Author

Antti Karttunen, Sep 04 2018

Status

approved