A328576 - OEIS

A328576

Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)], for all i, j.

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

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OFFSET

0,2

COMMENTS

Restricted growth sequence transform of function f, defined as: f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)].

For all i, j: a(i) = a(j) => A328114(i) = A328114(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base

PROG

(PARI)

up_to = 32768;

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; };

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557

A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };

A328575(n) = A003557(A032742(A276086(n)));

Aux328576(n) = if(!n, n, [A276088(n), A328575(n)]);

v328576 = rgs_transform(vector(1+up_to, n, Aux328576(n-1)));

A328576(n) = v328576[1+n];

CROSSREFS

Cf. A003557, A032742, A276086, A276088, A328114, A328575, A328577.

Sequence in context: A238892 A238279 A282933 * A052275 A338139 A244798

Adjacent sequences: A328573 A328574 A328575 * A328577 A328578 A328579

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 20 2019

STATUS

approved