files / problems / ulam-sequence / compute / bounds_table.json

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{
  "published_CS": 1.454,
  "eggleton": 1.4655712318767682,
  "barrier": 1.4146717609798722,
  "table": [
    {
      "L": 1,
      "F2": 5,
      "CF": 2.23606797749979,
      "C2": null,
      "wordF": "1",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 2,
      "F2": 9,
      "CF": 1.7320508075688772,
      "C2": null,
      "wordF": "21",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 3,
      "F2": 18,
      "CF": 1.6188704068605666,
      "C2": null,
      "wordF": "231",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 4,
      "F2": 37,
      "CF": 1.57045398358553,
      "C2": null,
      "wordF": "2313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 5,
      "F2": 69,
      "CF": 1.5271612967071428,
      "C2": null,
      "wordF": "23131",
      "beats_1.454": false,
      "beats_1.452": false,
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      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 6,
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      "CF": 1.5130857494229015,
      "C2": null,
      "wordF": "231313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 7,
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      "CF": 1.4955364496182528,
      "C2": null,
      "wordF": "2313131",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 8,
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      "CF": 1.4883814531348007,
      "C2": null,
      "wordF": "23131313",
      "beats_1.454": false,
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      "beats_1.445": false,
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      "beats_1.442": false
    },
    {
      "L": 9,
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      "CF": 1.4792404321608552,
      "C2": null,
      "wordF": "231313113",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
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    },
    {
      "L": 10,
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      "CF": 1.4728610936659952,
      "C2": null,
      "wordF": "2313131313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 11,
      "F2": 4710,
      "CF": 1.4687757574931937,
      "C2": null,
      "wordF": "23131311313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 12,
      "F2": 9252,
      "CF": 1.4630521870209818,
      "C2": null,
      "wordF": "231313131313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 13,
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      "CF": 1.459971644285427,
      "C2": null,
      "wordF": "2313131131313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 14,
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      "C2": null,
      "wordF": "23131311311313",
      "beats_1.454": false,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 15,
      "F2": 75172,
      "CF": 1.4539022327811069,
      "C2": 1.453902202043493,
      "wordF": "231313113131313",
      "beats_1.454": true,
      "beats_1.452": false,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 16,
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      "CF": 1.451408682527181,
      "C2": 1.4514086807307693,
      "wordF": "2313131131311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 17,
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      "CF": 1.4493008913297731,
      "C2": 1.449300889649942,
      "wordF": "23131311311311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 18,
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      "CF": 1.4475866441718164,
      "C2": 1.4475866437807043,
      "wordF": "231313113131311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 19,
      "F2": 1202020,
      "CF": 1.4454320364264808,
      "C2": 1.4454320349168224,
      "wordF": "2313131131313131313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": false,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 20,
      "F2": 2417294,
      "CF": 1.4440533449393822,
      "C2": 1.444053344850811,
      "wordF": "23131311311311311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": true,
      "beats_1.443": false,
      "beats_1.442": false
    },
    {
      "L": 21,
      "F2": 4845788,
      "CF": 1.442697712197638,
      "C2": null,
      "wordF": "231313113113131311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": true,
      "beats_1.443": true,
      "beats_1.442": false
    },
    {
      "L": 22,
      "F2": 9690750,
      "CF": 1.4413878263110487,
      "C2": null,
      "wordF": "2313131131313131311313",
      "beats_1.454": true,
      "beats_1.452": true,
      "beats_1.445": true,
      "beats_1.443": true,
      "beats_1.442": true
    }
  ],
  "N0_L16_1452": {
    "ok": true,
    "L": 16,
    "target": "1452/1000",
    "first_full_q": 101,
    "N0": 1607,
    "last_fail_n": 1606,
    "C_F": 1.451408682527181
  },
  "N0_L21_1443": {
    "ok": true,
    "L": 21,
    "target": "1443/1000",
    "first_full_q": 158,
    "N0": 3304,
    "last_fail_n": 3303,
    "C_F": 1.442697712197638
  },
  "N0_L22_1442": {
    "ok": true,
    "L": 22,
    "target": "1442/1000",
    "first_full_q": 75,
    "N0": 1635,
    "last_fail_n": 1634,
    "C_F": 1.4413878263110487
  },
  "v5_sq": 65,
  "note": "CF = (max ||W||_F^2)^{1/(2L)} is an exact integer-power quantity. N0 is the first index from which the CS majorant started at v_5=(6,4,3,2) is \u2264 (p/1000)^n by integer comparison."
}