A378604 Lexicographically earliest infinite sequence such that a(i) = a(j) => A033630(i) = A033630(j) and A083206(i) = A083206(j), for all i, j >= 1.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 7, 1, 1, 1, 8, 1, 9, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 8, 1, 3, 1, 1, 1, 11, 1, 1, 1, 1, 1, 9, 1, 1, 1, 12, 1, 13, 1, 1, 1, 1, 1, 14, 1, 15, 1, 1, 1, 16, 1, 1, 1, 2, 1, 17, 1, 1, 1, 1, 1, 18, 1, 1, 1, 4, 1, 14, 1, 2, 1

Offset

1,6

Comments

Restricted growth sequence transform of the ordered pair [A033630(n), A083206(n)].

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Prog

(PARI)
up_to = 100000;
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; };
v033630 = readvec("b033630_to.txt"); \\ Precomputed with A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A033630(n) = v033630[n];
v083206 = readvec("b083206_to.txt"); \\ Precomputed with A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
A083206(n) = v083206[n];
Aux378604(n) = [A033630(n), A083206(n)];
v378604 = rgs_transform(vector(up_to, n, Aux378604(n)));
A378604(n) = v378604[n];

Crossrefs

Cf. A033630, A083206.

Cf. also A378601, A378602, A378603.

Sequence in context: A033630 A308608 A371213 * A323719 A220122 A101446

Adjacent sequences: A378601 A378602 A378603 * A378605 A378608 A378610

Keyword

nonn,new

Author

Antti Karttunen, Dec 01 2024

Status

approved