{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R222",
  "content_hash": null,
  "slug": "dpi-artifact-million-starts",
  "type": "artifact",
  "title": "Loomis reports a million-start joining check",
  "summary": "Every start through one million was reported to join the orbit of 1.",
  "relevance": "For Merging of orbits under adding the product of nonzero digits, record dpi-artifact-million-starts (“Loomis reports a million-start joining check”) supplies evidence or a replay used to check the packet. The record states: Every start through one million was reported to join the orbit of 1.",
  "relevance_source": "recorded",
  "body": "Loomis reports testing every positive start at most one million. Each orbit joined the orbit beginning at 1. The first difficult start was 63, with the recorded identity\n\\[\nT^{322}(63)=150056=T^{261}(1).\n\\]\nThis is author-reported computation rather than a retained TheoremDB program.",
  "status": "sourced",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "every starting value from 1 through 1000000",
    "bounds": {
      "start": {
        "min": 1,
        "max": 1000000
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "artifact",
    "citation": {
      "url": "https://facstaff.bloomu.edu/ploomis/sequences.html",
      "locator": "Paul Loomis, Integer Sequences, section III, Sequences That Join; cross-referenced by OEIS A096287"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://facstaff.bloomu.edu/ploomis/sequences.html",
    "locator": "Paul Loomis, Integer Sequences, section III, Sequences That Join; cross-referenced by OEIS A096287"
  },
  "relations": [
    {
      "slug": "R224",
      "title": "Loomis conjectured that every orbit joins the orbit of 1",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "digit-product-iteration-trajectories",
      "title": "digit product iteration trajectories",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}