A119034 Numbers k such that the k-th triangular number contains only digits {0,1,2}.

1, 4, 6, 15, 20, 66, 141, 200, 473, 666, 2000, 6666, 14840, 15620, 20000, 49193, 66666, 154926, 200000, 494006, 666666, 2000000, 4939858, 6666666, 20000000, 66666666, 200000000, 200105073, 651307933, 666666666, 1563400141

Offset: 1

Author

Giovanni Resta, May 10 2006

Keywords

• nonn
• base

Comments

Cross-references to similar sequences:

012 A119034 013 A119036 014 A119038 015 A119040 016 A119042 017 A119044

018 A119046 019 A119048 023 A119050 024 A218389 025 A119052 026 A119054

027 A218398 028 A119056 029 A119058 034 A119060 035 A119062 036 A119064

037 A119066 038 A119068 039 A119070 045 A119072 046 A119074 047 A218400

048 A119076 049 A119078 056 A119080 057 A119082 058 A119084 059 A119086

067 A119088 068 A119090 069 A119092 078 A119094 079 A218402 089 A119096

123 A119098 124 A119100 125 A119102 126 A119104 127 A119106 128 A119108

129 A119110 134 A119112 135 A119114 136 A119116 137 A119118 138 A119120

139 A119122 145 A119124 146 A119126 147 A119127 148 A119129 149 A119131

156 A119133 157 A119135 158 A119137 159 A119139 167 A119141 168 A119143

169 A119145 178 A119147 179 A119149 189 A119151 234 ... (*) 235 A119153

236 A119155 237 ... (*) 238 A119157 239 ... (*) 245 A119159 246 A119161

247 ... (*) 248 A119163 249 ... (*) 256 A119165 257 A119167 258 A119169

259 A119171 267 A119173 268 A119175 269 A119177 278 A119179 279 ... (*)

289 A119181 345 A119183 346 A119185 347 ... (*) 348 ... (*) 349 ... (*)

356 A119187 357 A119189 358 A119191 359 A119193 367 A119195 368 A119197

369 A119199 378 A119201 379 ... (*) 389 ... (*) 456 A119203 457 A119205

458 A119207 459 A119209 467 A119211 468 A119213 469 A119215 478 A119217

479 ... (*) 489 ... (*) 567 A119219 568 A119221 569 A119223 578 A119225

579 A119227 589 A119229 678 A119231 679 A119233 689 A119235 789 A119237

(*) Searched up to T(x)<10^32, resulted in short sequences (#terms<4):

247,249,279,479,489->{}, 234,237,239,347,348,349,379,389->{2}

Links

• G. Resta, Tridigital Triangular Numbers

Crossrefs

Cf. A000217, A119033.

Programs

Magma

[n: n in [1..2*10^7] | Set(Intseq(Binomial(n+1, 2))) subset [0, 1, 2]]; // Vincenzo Librandi, Oct 07 2015

Mathematica

Select[Range[2 10^7], Complement[IntegerDigits[Binomial[# + 1, 2]], {0, 1, 2}] == {}&] (* Vincenzo Librandi, Oct 07 2015 *)