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Numbers k such that the k-th triangular number contains each of the 10 decimal digits exactly once.
2

%I #20 Jul 14 2021 10:02:32

%S 46097,49796,50139,55151,55484,56520,58050,62495,62567,62900,66294,

%T 68805,69542,70766,72594,73737,73971,74168,74357,75555,76364,77805,

%U 78686,78848,84555,85959,86076,87263,87669,88406,89883,90287,90297

%N Numbers k such that the k-th triangular number contains each of the 10 decimal digits exactly once.

%C There are 82 such numbers, the largest being 138959.

%C A118668(a(n)) = 10. - _Reinhard Zumkeller_, Jul 11 2015

%H Zak Seidov, <a href="/A115939/b115939.txt">Table of n, a(n) for n = 1..82</a> (full sequence)

%e T(75555) = 2854316790.

%t Select[Range[141000], Sort[IntegerDigits[# (# + 1)/2]] == Range[0, 9] &] (* _Giovanni Resta_, Mar 19 2013 *)

%t (Sqrt[8#+1]-1)/2&/@Select[FromDigits/@Select[Permutations[Range[0,9]], #[[1]]>0&],OddQ[Sqrt[8#+1]]&] (* _Harvey P. Dale_, Sep 19 2016 *)

%Y Cf. A000217, A115940, A118668.

%K nonn,base,fini,full

%O 1,1

%A _Giovanni Resta_, Feb 06 2006