A324531 -id:A324531 - cp's OEIS frontend

A324530 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A033879(n), A318458(n)] for all other numbers, except f(1) = -1.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 9, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 16, 28, 19, 29, 30, 31, 19, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 2, 39, 56, 57, 58, 35, 59, 60, 61, 62, 63, 64, 65, 51, 66, 67, 68, 41, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 51, 80

Offset: 1

Antti Karttunen, Mar 05 2019

nonn

Cf. A033879, A318458, A324389, A324400, A324531.

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; };
A033879(n) = (n+n-sigma(n));
A318458(n) = bitand(n,sigma(n)-n);
Aux324530(n) = if(1==n,-1,[A033879(n), A318458(n)]);
v324530 = rgs_transform(vector(up_to,n,Aux324530(n)));
A324530(n) = v324530[n];

a(2^n) = 2 for all n >= 1.

A324532 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A000120(n), A318458(n)] for all other numbers, except f(1) = 0.

Original entry on oeis.org

1, 2, 3, 2, 3, 4, 5, 2, 6, 7, 5, 6, 5, 8, 9, 2, 3, 10, 5, 11, 5, 12, 13, 6, 14, 15, 9, 16, 13, 17, 18, 2, 3, 6, 5, 19, 5, 12, 13, 20, 5, 21, 13, 22, 23, 17, 18, 6, 14, 21, 24, 25, 13, 26, 27, 14, 24, 28, 18, 29, 18, 30, 31, 2, 3, 32, 5, 6, 5, 33, 13, 34, 5, 35, 13, 36, 13, 37, 18, 38, 14, 14, 13, 39, 40, 41, 18, 42, 13, 43, 27, 44, 18, 45, 46, 6, 5, 36, 23, 47, 13

Offset: 1

Antti Karttunen, Mar 05 2019

nonn

Cf. A000120, A318458, A324530, A324531.

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; };
A318458(n) = bitand(n,sigma(n)-n);
Aux324532(n) = if(1==n,0,[hammingweight(n), A318458(n)]);
v324532 = rgs_transform(vector(up_to,n,Aux324532(n)));
A324532(n) = v324532[n];

For n >= 1, a(2^n) = 2.

A336157 Lexicographically earliest infinite sequence such that a(i) = a(j) => A318458(i) = A318458(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 2, 1, 4, 5, 2, 6, 2, 7, 8, 1, 2, 9, 2, 10, 11, 3, 2, 6, 4, 12, 13, 14, 2, 15, 2, 1, 11, 6, 11, 16, 2, 3, 11, 17, 2, 18, 2, 19, 20, 7, 2, 6, 4, 21, 22, 23, 2, 24, 22, 6, 22, 17, 2, 25, 2, 26, 27, 1, 11, 28, 2, 6, 11, 28, 2, 29, 2, 5, 30, 31, 11, 32, 2, 31, 33, 6, 2, 34, 35, 3, 11, 36, 2, 37, 22, 38, 11, 39, 40, 6, 2, 41, 20, 42, 2, 43, 2, 44, 45

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A318458(n), A336158(n)].
For all i, j:
  A324400(i) = A324400(j) => a(i) = a(j).
  A324401(i) = A324401(j) => a(i) = a(j).

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

Cf. A000265, A046523, A318458, A324400, A324401, A336158.

Cf. A324389, A324530, A324531, A324532 for other similar constructions (also similar by their scatter plots).

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A318458(n) = bitand(n, sigma(n)-n);
Aux336157(n) = [A318458(n), A336158(n)];
v336157 = rgs_transform(vector(up_to, n, Aux336157(n)));
A336157(n) = v336157[n];

cp's OEIS Frontend

A324530 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A033879(n), A318458(n)] for all other numbers, except f(1) = -1.

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A324532 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A000120(n), A318458(n)] for all other numbers, except f(1) = 0.

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A336157 Lexicographically earliest infinite sequence such that a(i) = a(j) => A318458(i) = A318458(j) and A336158(i) = A336158(j), for all i, j >= 1.

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