Numbers with equal rises and falls

Numbers with equal rises and falls is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

When a number is written in base 10, adjacent digits may "rise" or "fall" as the number is read (usually from left to right).
OEIS Sequence A296712 describes numbers whose digit sequence in base 10 have equal "rises" and "falls".
Definition:
Given the digits of the number are written as a series d:

• A rise is an index i such that d(i) < d(i+1)
• A fall is an index i such that d(i) > d(i+1).

Examples:

• The number 726169 has 3 rises and 2 falls, so it is not in the sequence.
• The number 83548 has 2 rises and 2 falls, so it is in the sequence.

Task

Print the first 200 numbers in the sequence. Show that the 10 millionth (10,000,000th) number in the sequence is 41909002.

See also: OEIS:https://oeis.org/A296712 the Oeis entry.

Julia

<lang julia>using Lazy

function rises_and_falls(n)

   if n < 10
       return 0, 0
   end
   lastr, rises, falls = n % 10, 0, 0
   while n != 0
       n, r = divrem(n, 10)
       if r > lastr
           falls += 1
       elseif r < lastr
           rises += 1
       end
       lastr = r
   end
   return rises, falls

end

isA296712(x) = ((a, b) = rises_and_falls(x); return a == b)

function genA296712(N, M)

   A296712 = filter(isA296712, Lazy.range(1));
   arr = take(N, A296712)
   j = 0
   for i in take(200, A296712)
       j += 1
       print(lpad(i, 4), j % 20 == 0 ? "\n" : "")
   end
   for i in take(M, A296712)
       j = i
   end
   println("\nThe $M-th number in sequence A296712 is $j.")

end

genA296712(200, 10_000_000)

</lang>

Output:

   1   2   3   4   5   6   7   8   9  11  22  33  44  55  66  77  88  99 101 102
 103 104 105 106 107 108 109 111 120 121 130 131 132 140 141 142 143 150 151 152
 153 154 160 161 162 163 164 165 170 171 172 173 174 175 176 180 181 182 183 184
 185 186 187 190 191 192 193 194 195 196 197 198 201 202 203 204 205 206 207 208
 209 212 213 214 215 216 217 218 219 222 230 231 232 240 241 242 243 250 251 252
 253 254 260 261 262 263 264 265 270 271 272 273 274 275 276 280 281 282 283 284
 285 286 287 290 291 292 293 294 295 296 297 298 301 302 303 304 305 306 307 308
 309 312 313 314 315 316 317 318 319 323 324 325 326 327 328 329 333 340 341 342
 343 350 351 352 353 354 360 361 362 363 364 365 370 371 372 373 374 375 376 380
 381 382 383 384 385 386 387 390 391 392 393 394 395 396 397 398 401 402 403 404

The 10000000-th number in sequence A296712 is 41909002.