A290094 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A289813(i)) = A278222(A289813(j)) and A278222(A289814(i)) = A278222(A289814(j)) for all i, j >= 0.

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

Offset

0,2

Comments

Restricted growth sequence transform of A290093, i.e., of the ordered pair [A290091(n), A290092(n)].

From Antti Karttunen, Oct 21 2025: (Start)

For all i, j >= 0:

A331303(i) = A331303(j) => a(i) = a(j),

a(i) = a(j) => A387188(i) = A387188(j) => A006047(i) = A006047(j) => A053735(i) = A053735(j).

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 0..59049

Prog

(PARI)
up_to = 59049;
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A278222(n) = A046523(A005940(1+n));
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
Aux290094(n) = [A278222(A289813(n)), A278222(A289814(n))];
v290094 = rgs_transform(vector(1+up_to, n, Aux290094(n-1)));
A290094(n) = v290094[1+n]; \\ Antti Karttunen, Oct 21 2025

Crossrefs

Cf. A005940, A046523, A289813, A289814.

Cf. A006047, A038574, A053735, A062756, A081603, A117942, A206424, A227428, A290091, A290092, A290079, A290093, A331303, A387188 for various related ternary (base-3) sequences.

Cf. also A278222, A286622 (analogous "filter" for base-2 related sequences), A305303, A305433, A340383, A365720.

Sequence in context: A286533 A172520 A387188 * A379633 A285904 A285714

Adjacent sequences: A290091 A290092 A290093 * A290095 A290096 A290097

Keyword

nonn,base,look

Author

Antti Karttunen, Jul 26 2017

Extensions

New definition added, old definition moved to the comments - Antti Karttunen, Oct 21 2025

Status

approved