A389901 - OEIS

A389901

Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(A126760(i)) = A007814(A126760(j)) and A007949(A126760(i)) = A007949(A126760(j)) for all i, j >= 1.

1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 4, 1, 1, 3, 2, 1, 5, 1, 1, 2, 3, 4, 6, 1, 7, 1, 1, 3, 2, 2, 1, 1, 4, 5, 8, 1, 1, 1, 1, 2, 2, 3, 3, 4, 2, 6, 9, 1, 1, 7, 5, 1, 10, 1, 1, 3, 1, 2, 4, 2, 3, 1, 3, 1, 2, 4, 1, 5, 6, 8, 11, 1, 1, 1, 7, 1, 2, 1, 12, 2, 1, 2, 4, 3, 1, 3, 2, 4, 5, 2, 1, 6, 1, 9, 13, 1, 3, 1, 4, 7, 2, 5, 1, 1, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Restricted growth sequence transform of the ordered pair [A007814(A126760(n)), A007949(A126760(n))].

LINKS

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

FORMULA

a(n) = A322026(A126760(n)), where A322026 is the ordinal transform of A126760, and vice versa.

PROG

(PARI)

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; };

A126760(n) = {n && n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2 };

A007814(n) = valuation(n, 2);

A007949(n) = valuation(n, 3);

Aux389901(n) = [A007814(A126760(n)), A007949(A126760(n))];

v389901 = rgs_transform(vector(up_to, n, Aux389901(n)));

A389901(n) = v389901[n];

(PARI)

A065331(n) = (3^valuation(n, 3)<<valuation(n, 2));

A071521(n) = { my(t=1/3); sum(k=0, logint(n, 3), t*=3; logint(n\t, 2)+1); };

A322026(n) = A071521(A065331(n));

A126760(n) = {n && n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2 };

A389901(n) = A322026(A126760(n));