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Numbers k such that the k-th triangular number contains only digits {1,3,4}.
2

%I #14 Mar 31 2023 00:50:12

%S 1,2,53,258,25746,53746,161946,7930238,14927378,29810546,4714751561,

%T 25742623453,94268917816334704578

%N Numbers k such that the k-th triangular number contains only digits {1,3,4}.

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/tr/tr134.html">Tridigital Triangular Numbers</a>.

%t (Sqrt[8#+1]-1)/2&/@Table[Select[FromDigits/@Tuples[{1,3,4},n],OddQ[ Sqrt[ 8#+1]]&],{n,21}]//Flatten (* _Harvey P. Dale_, Jul 09 2017 *)

%Y Cf. A000217, A119111. See A119034 for a table of cross-references.

%K nonn,base,more

%O 1,2

%A _Giovanni Resta_, May 10 2006

%E a(13) from _Tyler Busby_, Mar 30 2023