A366390 -id:A366390 - cp's OEIS frontend

A366392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366390(i) = A366390(j) for all i, j >= 1, where A366390 is the Dirichlet inverse of A366389.

1, 2, 3, 4, 5, 6, 7, 4, 4, 8, 9, 4, 10, 11, 12, 4, 13, 4, 14, 4, 15, 16, 17, 4, 6, 18, 4, 4, 19, 20, 21, 4, 22, 23, 24, 4, 25, 26, 27, 4, 28, 29, 30, 31, 4, 32, 33, 4, 34, 35, 36, 37, 38, 4, 39, 4, 40, 41, 42, 4, 43, 44, 4, 4, 45, 46, 47, 4, 48, 49, 50, 4, 51, 52, 53, 4, 54, 55, 56, 4, 57, 58, 59, 4, 60, 61, 15, 62

Offset: 1

Antti Karttunen, Oct 22 2023

nonn

Restricted growth sequence transform of A366390.

For all i, j: a(i) = a(j) => A365428(i) = A365428(j) => A359377(i) = A359377(j).

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

Cf. A010872, A030101, A057889, A073675, A359377, A365428, A366389, A366390.

Cf. also A366293.

\\ Needs also program given in A366389:
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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA366389(n))));
A366392(n) = v366392[n];

A366389 Variant of bijective bit-reverse of n (A057889) for which it holds that a(n) == n (mod 3).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 12, 22, 14, 15, 16, 17, 18, 25, 20, 21, 13, 29, 24, 19, 11, 27, 28, 23, 30, 31, 32, 33, 34, 98, 36, 82, 50, 57, 40, 74, 42, 106, 104, 45, 58, 122, 48, 70, 38, 51, 88, 86, 54, 118, 56, 39, 46, 110, 60, 94, 62, 63, 64, 65, 66, 97, 68, 81, 49, 113, 72, 73, 41, 105, 100, 89, 114, 121

Offset: 0

Antti Karttunen, Oct 22 2023

Like A057889, also this is a self-inverse permutation of nonnegative integers.

Cf. A010872, A030101, A057889, A073675, A366378, A366379, A366390 (Dirichlet inverse), A366392.

Cf. also A118967.

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A073675(n) = if(valuation(n,2)%2,n/2,2*n);
A366389(n) = { my(u=A057889(n)); if(!((u-n)%3),u,A073675(u)); };

If A057889(n) == n mod 3, then a(n) = A057889(n), otherwise a(n) = A073675(A057889(n)) = A057889(A073675(n)).

For all n >= 0, A010872(a(n)) = A010872(n).

cp's OEIS Frontend

A366392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366390(i) = A366390(j) for all i, j >= 1, where A366390 is the Dirichlet inverse of A366389.

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