A119033 - OEIS

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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..210^7] \| 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 January 30 05:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)