Sequence A37XX

[Bruno Paiva]

Earlier I tried uploading this sequence suggestion, but since I'm new to this and it's my first time, I'm not sure if I did it correctly. When I saved the changes, nothing appeared; it just refreshed the page.Can anyone tell me if I did this correctly?

%ID: A37XXXX (Reservado para o OEIS)
%N: Number of genuine directed cycles (length >= 3) in the semiprime transition graph G for semiprimes up to N.
%K nonn, walk, more, gpn
%O: 1,1
%A: Bruno Paiva Viana, Sep 30 2026
%F:
A integer sequence where a(n) represents the total count of unique genuine cycles (cycles with length greater than or equal to 2 nodes, excluding bidirectional mirror pairs) formed by valid modular transitions (w, x, y, z) between decomposed semiprimes N.
%D:
In number theory and graph models constructed via 2N49R1M3 transition dynamics, each node represents a decomposed semiprime N = p \cdot q. Directed edges (N_1, N_2) exist if N_2 satisfies valid modular tuple conditions derived from N_1. Mirror cycles are defined as reciprocal transitions N_1 \leftrightarrow N_2 (length 2), while genuine cycles correspond to directed paths N_1 \to N_2 \to \dots \to N_k \to N_1 with k \ge 3.
%E:
1, 0, 2, 5, 12, 29, 74
%C:
The graph G is built as a networkx.DiGraph() using valid next semiprime transitions.
The search algorithm uses Depth-First Search (DFS) to detect recursion stack intersections and classify cycles by topological length.
Mirror cycles are filtered out using bidirectional edge validation has_edge(u,v) and has_edge(v,u).

import networkx as nx

def generate_oeis_cycle_sequence(df_full_analysis, df_full_analysis_indexed):
    G_multi_edge = nx.DiGraph()

    for N_val in df_full_analysis['N'].unique():
        if N_val in df_full_analysis_indexed.index:
            next_N_candidates = get_all_valid_next_N_primes(N_val)
            for next_N in next_N_candidates:
                G_multi_edge.add_edge(N_val, next_N)

    def find_cycles_dfs(graph):
        all_cycles = []
        path = []
        visited = set()
        recursion_stack = set()

        def dfs(u):
            visited.add(u)
            recursion_stack.add(u)
            path.append(u)

            for v in graph.neighbors(u):
                if v not in visited:
                    dfs(v)
                elif v in recursion_stack:
                    cycle_start_index = path.index(v)
                    cycle = path[cycle_start_index:]
                    all_cycles.append(tuple(cycle))

            path.pop()
            recursion_stack.remove(u)

        for node in graph.nodes():
            if node not in visited:
                dfs(node)

        return all_cycles

    cycles_multi_edge = find_cycles_dfs(G_multi_edge)

    ciclos_espelho_multi = []
    ciclos_genuinos_multi = []

    for cycle in cycles_multi_edge:
        if len(cycle) == 2:
            n1, n2 = cycle[0], cycle[1]
            if G_multi_edge.has_edge(n1, n2) and G_multi_edge.has_edge(n2, n1):
                if tuple(sorted(cycle)) not in [tuple(sorted(c)) for c in ciclos_espelho_multi]:
                    ciclos_espelho_multi.append(cycle)
        elif len(cycle) >= 3:
            if tuple(cycle) not in ciclos_genuinos_multi:
                ciclos_genuinos_multi.append(cycle)

    return len(ciclos_genuinos_multi)

[Michel Marcus]

A37XXXX  : is not a valid A-number.

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[Bruno Paiva]

Excuse my ignorance, I'm new and have no experience. Since I couldn't find that specific sequence, what number should I put? Could you send me a link that explains this A classification?I'm a little lost

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAFxT7zW-TJP_FvZV3iyevRsU5ex%3D-jC-w10v7TM7pYV3tAa1KQ%40mail.gmail.com.

[Tom Duff]

An A number is a serial number. They’re assigned sequentially to new sequences. To find a particular sequence, enter its first few terms in the search box on the home page. You can enter anything in the search box, like “Catalan numbers”, not just sequence terms. 

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CA%2Be0518LLm2tdgW%2B%3D8U5ejbqvNYXjjbjbPkKH1dHQaG-%3Dn6msQ%40mail.gmail.com.

[Sean A. Irvine]

Hi Bruno,

After logging in to the OEIS, start here:

https://oeis.org/Submit.html

See also:

https://oeis.org/wiki/Overview_of_the_contribution_process

The content you pasted into the email looks like an incorrect mixture of internal format and ordinary text. Instead (at least for the first few sequences) manually paste the relevant text into each of the fields in the submission box.

Regards,

Sean.

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[Bruno Paiva]

Thank you, I had only skimmed it, I will read it completely and reflect on it. 

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAL0FETnVCBOUsVdmd4APA-qmVV6u%3DJDEym8m-V%2BD%3D%3DbprDQiXQ%40mail.gmail.com.