[seqfan] Re: Last two digits added --> new integer rhymes

Jim Nastos nastos at gmail.com
Sat Feb 15 08:16:11 CET 2014


Eric,
  It is still a nice sequence. Here are 500 terms.
J

1 2 3 5 8 13 4 7 11 12 23 15 6 111 22 14 25 17 18 9 117 28 10 21 33 16 27
19 110 31 24 26 38 211 32 35 48 112 43 37 210 41 45 29 311 42 36 39 212 53
58 113 34 47 411 52 57 312 63 49 213 44 68 114 55 310 51 46 410 61 67 313
54 59 214 65 511 62 78 115 56 611 72 69 215 66 412 73 510 71 88 116 77 314
75 512 83 711 82 610 81 79 216 87 315 76 413 64 710 91 810 101 121 93 612
103 123 85 513 74 811 92 911 102 122 84 712 133 86 414 95 514 105 125 97
316 107 127 89 217 98 317 108 118 99 218 109 119 910 131 94 613 104 124 96
415 106 126 128 1010 141 135 138 1011 132 145 129 1111 142 136 139 812 143
137 1110 151 146 1210 161 147 1211 152 157 912 153 148 1012 163 149 713 134
167 813 144 158 913 154 159 614 155 1310 171 168 714 165 1311 162 178 515
156 1411 172 169 615 166 1112 173 1410 181 179 416 177 814 175 1212 183
1511 182 1510 191 1610 201 221 193 1312 203 223 185 1013 164 1710 231 174
1611 192 1711 202 222 184 1412 233 176 1113 194 1213 204 224 186 914 195
1014 205 225 187 715 196 815 206 226 188 516 197 616 207 227 189 417 198
517 208 228 1810 241 235 238 1811 232 245 199 318 209 219 1910 251 236 229
1911 242 246 2010 261 237 2110 271 248 1512 243 247 2011 252 257 1612 253
258 1313 234 267 1413 244 268 1114 255 2210 281 239 1712 263 249 1513 254
259 1214 265 2111 262 278 915 256 2211 272 269 1015 266 1812 273 2310 291
2410 301 321 283 2311 282 2510 331 264 2610 341 275 1912 293 2012 303 323
285 1613 274 2411 292 2511 302 322 284 2112 333 276 1713 294 1813 304 324
286 1314 295 1414 305 325 277 1514 335 288 716 287 1115 296 1215 306 326
298 617 308 328 2710 351 336 279 816 297 916 307 327 289 717 338 2611 332
345 299 418 309 319 2810 361 337 2910 371 348 2212 343 347 2711 342 346
3010 381 329 2811 352 357 2312 353 358 1913 334 367 2013 344 368 1614 355
3110 391 3210 401 421 363 339 2412 373 3310 431 354 349 2113 364 3410 441
365 2911 362 378 1315 356 3011 372 359 1714 375 2512 383 3111 382 3510 451
366 2612 393 2712 403 423 385 2213 374 3211 392 3311 402 422 384 2812


On Fri, Feb 14, 2014 at 3:20 PM, Eric Angelini <Eric.Angelini at kntv.be>wrote:

> > it is not a permutation of the Naturals. For instance, 100 (or any
> number ending in "100") does not appear in this sequence since the last two
> digits of S will never sum to 0, 00, or 100
>
> ... Jim Nastos is right, sorry...
> Shame on me...
> My first attempt to produce a permutation
> failed too; I had tried the sequence
> where the word "ending", hereunder,
> was replaced by "beginning".
> Didn't check enough, though, the
> "new" definition...
>
>
> > Le 14 févr. 2014 à 20:23, "Eric Angelini" <Eric.Angelini at kntv.be> a
> écrit :
> >
> >
> > Hello SeqFans,
> > here is another nice permutation of the Naturals;
> >
> > S=1,2,3,5,8,13,4,7,11,12,23,15,6,111,
> > 22,14,25,17,18,9,117,28,10,21,33,16,
> > 27,19,110,31,...
> >
> > a(1)=1
> > a(2)=2
> > a(n) is the smallest integer not yet in S
> > ending with the sum of the last two digits
> > of S.
> >
> > We see after 13 that S was extended with 4
> > as 1+3=4 and 4 was not yet in S;
> >
> > We see after 4 that S was extended with 7
> > as 3+4=7 and 7 was not yet in S;
> >
> > We see after 7 that S was extended with 11
> > as 4+7=11 and 11 was not yet in S;
> >
> > We see after 11 that S was extended with 12
> > as 1+1=2 and 2 being already in S was replaced by 12, smallest integer
> > not yet in S and ending with "2";
> >
> > We see after 12 that S was extended with 23
> > as 1+2=3 and 3 being already in S, as 13, we used the smallest integer
> > not yet in S and ending with "3";
> > ...
> > Best,
> > É.
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
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>
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