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Numbers k such that the k-th triangular number contains only digits {0,1,8}.
2

%I #13 Sep 08 2022 08:45:25

%S 1,4,46,126,141,404,466,1541,4004,4195,4666,12658,13266,40004,41995,

%T 46666,147024,400004,402760,466666,1272798,1327266,1332666,4000004,

%U 4666666,40000004,46666666,133272666,133326666,148329375,400000004

%N Numbers k such that the k-th triangular number contains only digits {0,1,8}.

%H G. Resta, <a href="http://www.numbersaplenty.com/tr/tr018.html">Tridigital Triangular Numbers</a>

%t Select[Range[2 10^7], Complement[IntegerDigits[Binomial[# + 1, 2]], {0, 1, 8}] == {} &] (* _Vincenzo Librandi_, Dec 25 2015 *)

%o (Magma) [n: n in [1..4*10^6] | Set(Intseq(Binomial(n+1, 2))) subset [0, 1, 8]]; // _Vincenzo Librandi_, Dec 25 2015

%Y Cf. A000217, A119045. See A119034 for a table of cross-references.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, May 10 2006