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

1,3

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

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; };
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];

Crossrefs

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

Sequence in context: A331743 A366802 A178804 * A242112 A211316 A280226

Adjacent sequences: A322352 A322353 A322354 * A322356 A322357 A322358

Keyword

nonn

Author

Antti Karttunen, Dec 05 2018

Status

approved