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CLAUDE.md

This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.

Overview

This repository is a research workspace for studying sequences in OEIS. Each file computes, verifies, or explores a specific OEIS sequence. The primary languages used are Ruby (151 files), Python (100 files), and PARI/GP (96 files).

Running Code

# PARI/GP — run interactively
gp

# PARI/GP — load a file in the PARI session
\r path/to/file.gp

# PARI/GP — run from the terminal (outputs b-file to current directory)
gp < file.gp

# Ruby
ruby file.rb

# Python
python3 file.py

File Naming Convention

Files follow the pattern NNNNNN_VV.ext where NNNNNN is the zero-padded OEIS sequence number (without the leading A) and VV is a two-digit version number starting at 01. Example: 340295_01.gp is the first version of sequence A340295.

PARI/GP Style

  • G.f. (ordinary generating function) template: 
    my(N=66, x='x+O('x^N)); Vec(...)
  • E.g.f. (exponential generating function) template: 
    my(N=66, x='x+O('x^N)); Vec(serlaplace(...))
  • Helper functions use lowercase names (e.g., a354339(n), a_vector(n)).
  • For recursive sequences, accumulate results in a vector rather than calling recursively each time — recursion is slow.
  • Avoid using N as a variable name inside .gp files intended for \r loading; N is often already set interactively at the terminal.
  • When verifying an alternative formula, keep both computations in the same file and print the equality check (e.g., a(n) == b(n)).
  • Vec(f) returns coefficients in descending order; use Vecrev or polcoef when you need a specific coefficient.
  • Set default(realprecision, 1000) when using trigonometric/exponential expressions that require high precision.

Ruby Style

  • Indent with 2 spaces.
  • Use {|block|} style for short blocks, do...end for multiline.
  • Iteration typically uses .each, .map, n.times, (a..b).each.
  • Arrays are 1-indexed conceptually (prepend a dummy 0 element when mapping OEIS 1-based sequences to Ruby arrays).
  • Output: use p for debugging/inspection, print1-style comma-separated output is done with print + manual joining or puts.
  • Shared utilities live in linear/linear.rb; load with require './linear'.

Python Style

  • No imports beyond the standard library except where a specific library is needed (e.g., from graphillion import GraphSet in graphillion/).
  • Functions follow the OEIS sequence name or a descriptive lowercase name.
  • Output is printed with print([...]) for a list of terms.
  • Graphillion files begin with the comment # Using graphillion.

Key Shared Libraries

  • linear/linear.rb — Berlekamp-Massey algorithm, modular arithmetic (mod_inv, chinese), linear recurrence utilities (polynomial, reccurence_form).

Important Notes from src/README.md

Code is also maintained in separate repositories organized by sequence number: OEIS_00 through OEIS_04. This repo focuses on topic-based organization.

PARI b-file Generation

Run gp from the directory containing the .gp file so that write(...) outputs to the current directory:

cd path/to/dir && gp < file.gp

Inside the file, use a local variable (not N) for the upper limit:

M=100;
v = v(M);
for(n=0, M, write("bXXXXXX.txt", n, " ", polcoef(v, n)))

OEIS Edit Conventions

  • When a value is undefined/missing: use -1, not 0 (easier to search).
  • PARI function names: lowercase.
  • G.f. description format: Expansion of ... or Generating function Sum_{n >= 0} a(n)*x^n = ... (not G.f. ...).
  • Square array notation: T(n,k) preferred, though A(n,k) is acceptable.
  • Caution: in interactive PARI, variables persist across commands — avoid reusing constant names between sessions.