A304101 -id:A304101 - cp's OEIS frontend

A318832 Restricted growth sequence transform of A278222(A000203(n)).

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

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A000203(n).

For all i, j: a(i) = a(j) => A175548(i) = A175548(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A278222.

Cf. also A286622, A304101, A318831.

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));
v318832 = rgs_transform(vector(up_to,n,A278222(sigma(n))));
A318832(n) = v318832[n];

A374201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A048679(A328845(i))) = A278222(A048679(A328845(j))), for all i, j >= 1, where A328845 is a Fibonacci-based variant of the arithmetic derivative.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jul 02 2024

nonn

Restricted growth sequence transform of A278222(A048679(A328845(n))), or equally, of A304101(A328845(n)).
Related to the Zeckendorf-representation (A014417) of A328845(n).
For all i, j >= 0: a(i) = a(j) => A328847(i) = A328847(j).

Antti Karttunen, Table of n, a(n) for n = 0..75025

Cf. A000045, A014417, A048679, A278222, A304101, A328845, A328847.

Cf. also A304105, A373982.

up_to = 75025;
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) = { my(s=0, i=0); while(n, if(2!=(n%4), s += (n%2)<>= 1); (s); };
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]); };
A278222(n) = A046523(A005940(1+n));
A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1]));
v374201 = rgs_transform(vector(1+up_to, n, A278222(A048679(A328845(n-1)))));
A374201(n) = v374201[1+n];

cp's OEIS Frontend

A318832 Restricted growth sequence transform of A278222(A000203(n)).

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