OFFSET
1,2
COMMENTS
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
LINKS
Giovanni Resta, Tridigital Triangular Numbers.
FORMULA
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
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, May 10 2006
EXTENSIONS
a(24)-a(25) from Vincenzo Librandi, Dec 18 2015
STATUS
approved