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A119033
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Triangular numbers composed of digits {0,1,2}.
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113
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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
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OFFSET
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1,2
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COMMENTS
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Cross-references to similar sequences:
Entries marked "{ }" correspond to empty sequences: for every triangular number t, the residue t mod 100 contains at least one digit other than the three specified digits.
Entries marked "{3}" correspond to sequences containing only the single term 3: for every triangular number t != 3, the residue t mod 100 contains at least one digit other than the three specified digits.
(Proof: No triangular number ends in 2, 4, 7, or 9; every triangular number ending in 8 ends in 28 or 78; every triangular number ending in 3, other than the single-digit triangular number 3, ends in 03 or 53.) [Edited by Jon E. Schoenfield, May 02 2023]
Note that the first 36 sequences that are listed above do not contain "0" as the 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
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LINKS
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FORMULA
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MATHEMATICA
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Rest[Select[FromDigits/@Tuples[{0, 1, 2}, 10], IntegerQ[(Sqrt[8 # + 1] - 1)/2] &]] (* Vincenzo Librandi, Dec 18 2015 *)
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PROG
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(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
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CROSSREFS
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Cf. A213516 (triangular numbers having only two different digits).
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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