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A119033 Triangular numbers composed of digits {0,1,2}. 113
1, 10, 21, 120, 210, 2211, 10011, 20100, 112101, 222111, 2001000, 22221111, 110120220, 122000010, 200010000, 1210000221, 2222211111, 12001110201, 20000100000, 122021211021, 222222111111, 2000001000000, 12201101000011, 22222221111111, 200000010000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Cross-references to similar sequences:

012 A119033 013 A119035 014 A119037 015 A119039 016 A119041 017 A119043

018 A119045 019 A119047 023 A119049 024 A218390 025 A119051 026 A119053

027 A218397 028 A119055 029 A119057 034 A119059 035 A119061 036 A119063

037 A119065 038 A119067 039 A119069 045 A119071 046 A119073 047 A218399

048 A119075 049 A119077 056 A119079 057 A119081 058 A119083 059 A119085

067 A119087 068 A119089 069 A119091 078 A119093 079 A218401 089 A119095

123 A119097 124 A119099 125 A119101 126 A119103 127 A119105 128 A119107

129 A119109 134 A119111 135 A119113 136 A119115 137 A119117 138 A119119

139 A119121 145 A119123 146 A119125 147 A079654 148 A119128 149 A119130

156 A119132 157 A119134 158 A119136 159 A119138 167 A119140 168 A119142

169 A119144 178 A119146 179 A119148 189 A119150 234 ... (*) 235 A119152

236 A119154 237 ... (*) 238 A119156 239 ... (*) 245 A119158 246 A119160

247 ... (*) 248 A119162 249 ... (*) 256 A119164 257 A119166 258 A119168

259 A119170 267 A119172 268 A119174 269 A119176 278 A119178 279 ... (*)

289 A119180 345 A119182 346 A119184 347 ... (*) 348 ... (*) 349 ... (*)

356 A119186 357 A119188 358 A119190 359 A119192 367 A119194 368 A119196

369 A119198 378 A119200 379 ... (*) 389 ... (*) 456 A119202 457 A119204

458 A119206 459 A119208 467 A119210 468 A119212 469 A119214 478 A119216

479 ... (*) 489 ... (*) 567 A119218 568 A119220 569 A119222 578 A119224

579 A119226 589 A119228 678 A119230 679 A119232 689 A119234 789 A119236

(*) 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->{3}

Note that first 36 sequences that are listed in above do not contain "0" as a first term although 0 is a triangular number. In other words, sequences focus on the positive triangular numbers. - Altug Alkan, May 02 2016

a(n) == 1 or a(n) == 0 mod 10. - Chai Wah Wu, Nov 30 2018

LINKS

Table of n, a(n) for n=1..25.

G. Resta, Tridigital Triangular Numbers

MATHEMATICA

Rest[Select[FromDigits/@Tuples[{0, 1, 2}, 10], IntegerQ[(Sqrt[8 # + 1] - 1)/2] &]] (* Vincenzo Librandi, Dec 18 2015 *)

PROG

(MAGMA) [t: n in [1..2*10^7] | Set(Intseq(t)) subset {0, 1, 2} where t is n*(n+1) div 2]; // Vincenzo Librandi, Dec 18 2015

(PARI) isok(n) = ispolygonal(n, 3) && (vecmax(digits(n)) <= 2); \\ Michel Marcus, Dec 18 2015

CROSSREFS

Cf. A000217, A058412, A119034.

Cf. A213516 (triangular numbers having only two different digits).

Sequence in context: A306208 A001739 A072805 * A171067 A121807 A133163

Adjacent sequences:  A119030 A119031 A119032 * A119034 A119035 A119036

KEYWORD

nonn,base

AUTHOR

Giovanni Resta, May 10 2006

EXTENSIONS

a(24)-a(25) from Vincenzo Librandi, Dec 18 2015

STATUS

approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)