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Numbers k such that the k-th triangular number contains only digits {0,1,4}.
2

%I #16 Sep 08 2022 08:45:25

%S 1,4,141,144,286,9055,16795,44944,90598,167579,15100424,29678424,

%T 45637726,283245880,5291767266,1442505046119,45042455839799,

%U 151069595909375,14429213707617199,90999011435291333

%N Numbers k such that the k-th triangular number contains only digits {0,1,4}.

%C Next term must be greater than 4.4*10^18.

%H G. Resta, <a href="http://www.numbersaplenty.com/tr/tr014.html">Tridigital Triangular Numbers</a>

%t Select[Range[2 10^7], Complement[IntegerDigits[Binomial[# + 1, 2]], {0, 1, 4}] == {}&] (* _Vincenzo Librandi_, Oct 07 2015 *)

%o (Magma) [n: n in [1..2*10^7] | Set(Intseq(Binomial(n+1, 2))) subset [0, 1, 4]]; // _Vincenzo Librandi_, Oct 07 2015

%Y Cf. A000217, A119037. See A119034 for a table of cross-references.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, May 10 2006

%E Two more terms from _Max Alekseyev_, Jul 11 2009