A340680 -id:A340680 - cp's OEIS frontend

A341355 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1 and for n > 1, f(n) = [A341353(n), A341353(2*n)].

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

Offset: 1

Antti Karttunen, Feb 14 2021

nonn

For all i, j: a(i) = a(j) => A329903(i) = A329903(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A007949, A156552, A329903, A341353, A341354.

Cf. also A331304, A340680.

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; };
A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A341353(n) = A007949(A156552(n));
Aux341355(n) = if(1==n,1, [A341353(n), A341353(2*n)]);
v341355 = rgs_transform(vector(up_to, n, Aux341355(n)));
A341355(n) = v341355[n];

A353277 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A020639(n), A341353(n)], with f(1) = 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 2, 6, 2, 7, 8, 9, 2, 10, 2, 3, 4, 11, 2, 12, 2, 13, 4, 14, 2, 15, 2, 3, 2, 16, 4, 17, 2, 3, 4, 5, 18, 19, 2, 7, 4, 20, 2, 21, 2, 3, 18, 22, 2, 23, 2, 3, 2, 24, 2, 25, 2, 7, 2, 26, 2, 27, 4, 3, 8, 5, 4, 28, 2, 3, 2, 29, 2, 30, 2, 3, 2, 6, 2, 31, 2, 7, 4, 32, 4, 15, 2, 33, 18, 34, 8, 35, 2, 3, 8, 5, 2

Offset: 1

Antti Karttunen, Apr 10 2022

nonn

Restricted growth sequence transform of function f(1) = 1, and for n > 1, f(n) = [A007814(u), A007949(u)], where u = A156552(n).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A007814, A007949, A020639, A156552, A341353, A353278 (ordinal transform).

Cf. also A322026, A340680, A341355.

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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
Aux353277(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]);
v353277 = rgs_transform(vector(up_to, n, Aux353277(n)));
A353277(n) = v353277[n];

cp's OEIS Frontend

A341355 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1 and for n > 1, f(n) = [A341353(n), A341353(2*n)].

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