A322355 Lexicographically earliest such sequence a that a(i) = a(j) => A322351(i) = A322351(j) and A322352(i) = A322352(j), for all i, j.

1, 1, 2, 2, 3, 2, 4, 3, 5, 3, 6, 7, 8, 4, 9, 9, 10, 5, 11, 12, 8, 6, 13, 12, 14, 8, 15, 16, 17, 9, 18, 10, 19, 10, 20, 16, 21, 11, 20, 22, 23, 8, 24, 25, 26, 13, 27, 28, 29, 14, 30, 31, 32, 15, 23, 33, 21, 17, 34, 28, 35, 18, 36, 30, 37, 19, 38, 39, 40, 20, 41, 31, 42, 21, 43, 44, 35, 20, 45, 46, 47, 23, 48, 31, 49, 24, 50, 51, 52, 26, 42, 53, 35, 27, 42, 39, 54, 29

Offset: 1

Author

Antti Karttunen, Dec 05 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A322351(n), A322352(n)].

Essentially also the restricted growth sequence transform of the unordered pair {A003557(n), A173557(n)}.

For all i, j:

A295887(i) = A295887(j) => a(i) = a(j),

a(i) = a(j) => A322320(i) = A322320(j),

a(i) = a(j) => A322321(i) = A322321(j),

a(i) = a(j) => A000010(i) = A000010(j).

Links

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

Crossrefs

Cf. A000010, A003557, A173557, A295887, A322320, A322321, A322351, A322352.

Programs

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A322351(n) = min(A003557(n), A173557(n));
A322352(n) = max(A003557(n), A173557(n));
v322355 = rgs_transform(vector(up_to, n, [A322351(n), A322352(n)]));
A322355(n) = v322355[n];