c = 55

*(1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, 407, 409, 411, 500, 501, 504, 505, 506, 507, 509, 511, 600, 601, 604, 605, 606, 607, 609, 611, 700, 701, 704, 705, 706, 707, 709, 711, 900, 901, 904, 905, 906, 907, 909, 911)*

x = 10

*(10^6, 10^9, 10^15, 10^30, 10^33, 10^36, 10^39, 10^48, 10^51, 10^60)*

o = 7

*(2, 102, 402, 502, 602, 702, 902)*

So we have 56^10*7 = 2123138423672799232.

The latest version of Mathematica has a built-in

**IntegerName**function that does both cardinals and ordinals:

*count1[ncard_] :=*

*Length[Select[Range[10^(ncard - 1), 10^ncard - 1],*

*StringFreeQ[IntegerName[#, "Words"], "t"] &]];*

*m = {count1[1], count1[2], count1[3]}*

{6, 1, 48}

... The number of t-free cardinals of 1-digit, 2-digit, and 3-digit base-ten numbers.

*count2[nord_] :=*

*Length[Select[Range[10^(nord - 1), 10^nord - 1],*

*StringFreeQ[IntegerName[#, "Ordinal"], "t"] &]];*

*s = {count2[1], count2[2], count2[3]}*

{1, 0, 6}

... The number of t-free ordinals of 1-digit, 2-digit, and 3-digit base-ten numbers.

*Do[If[StringFreeQ[IntegerName[10^(3*i), "Words"], "t"],*

*s = Join[s, m*Total[s]], s = Join[s, {0, 0, 0}]], {i, 21}]; s*

{1, 0, 6, 0, 0, 0, 42, 7, 336, 2352, 392, 18816, 0, 0, 0, 131712, 21952, 1053696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7375872, 1229312, 59006976, 413048832, 68841472, 3304390656, 23130734592, 3855122432, 185045876736, 1295321137152, 215886856192, 10362569097216, 0, 0, 0, 0, 0, 0, 72537983680512, 12089663946752, 580303869444096, 4062127086108672, 677021181018112, 32497016688869376, 0, 0, 0, 0, 0, 0, 227479116822085632, 37913186137014272, 1819832934576685056, 0, 0, 0}

... The number of t-free ordinals of 1-digit to 66-digit base-ten numbers. Finally:

*Total[s]*

2123138423672799232

*IntegerName[%, "Words"]*

two quintillion, one hundred twenty-three quadrillion, one hundred thirty-eight trillion, four hundred twenty-three billion, six hundred seventy-two million, seven hundred ninety-nine thousand, two hundred thirty-two

Interestingly, Mathematica has attempted to bridge the gap between the dictionary large-number names up to 10^63 (one vigintillion) and the next dictionary entry at 10^303 (one centillion):

*Table[{i, IntegerName[10^i, "Words"]}, {i, 63, 306, 3}] // TableForm*

63 one vigintillion

66 one unvigintillion

69 one duovigintillion

72 one trevigintillion

75 one quattuorvigintillion

78 one quinvigintillion

81 one sexvigintillion

84 one septenvigintillion

87 one octovigintillion

90 one novemvigintillion

93 one trigintillion

96 one untrigintillion

99 one duotrigintillion

102 one trestrigintillions

105 one quattuortrigintillions

108 one quintrigintillions

111 one sextrigintillions

114 one septrigintillions

117 one octotrigintillions

120 one novemtrigintillions

123 one quadragintillions

126 one unquadragintillions

129 one duoquadragintillions

132 one tresquadragintillions

135 one quattuorquadragintillions

138 one quinquadragintillions

141 one sexquadragintillions

144 one septenquadragintillions

147 one octoquadragintillions

150 one novemquadragintillions

153 one quinquagintillions

156 one unquinquagintillions

159 one duoquinquagintillions

162 one tresquinquagintillions

165 one quattuorquinquagintillions

168 one quinquinquagintillions

171 one sexquinquagintillions

174 one septenquinquagintillions

177 one octoquinquagintillions

180 one novemquinquagintillions

183 one sexagintillions

186 one unsexagintillions

189 one duosexagintillions

192 one tresexagintillions

195 one quattuorsexagintillions

198 one quinsexagintillions

201 one sesexagintillions

204 one septensexagintillions

207 one octosexagintillions

210 one novemsexagintillions

213 one septuagintillions

216 one unseptuagintillions

219 one duoseptuagintillions

222 one treseptuagintillions

225 one quattuorseptuagintillions

228 one quinseptuagintillions

231 one seseptuagintillions

234 one septenseptuagintillions

237 one octoseptuagintillions

240 one novemseptuagintillions

243 one octogintillions

246 one unoctogintillions

249 one duooctogintillions

252 one tresoctogintillions

255 one quattuoroctogintillions

258 one quintoctogintillions

261 one sexoctogintillions

264 one septenoctogintillions

267 one octoctogintillions

270 one novoctogintillions

273 one nonagintillions

276 one unonagintillions

279 one duononagintillions

282 one trenonagintillions

285 one quattuornonagintillions

288 one quinonagintillions

291 one senonagintillions

294 one septenonagintillions

297 one octononagintillions

300 one novenonagintillions

303 one centillions

306 one billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion billion

Notice the terminal "s" for 10^102 to 10^303. I've alerted Wolfram to the bug. Then, starting at 10^306, all hell breaks loose!

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