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Numbers k such that k = n-th triangular number and last digits of k match n.
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%I #16 Mar 13 2015 00:59:36

%S 1,15,325,195625,43959376,4106490625,396606890625,25271617109376,

%T 83084112890625,22661209212890625,1596879961787109376,

%U 3344565630081787109376,1795096118003159918212890625

%N Numbers k such that k = n-th triangular number and last digits of k match n.

%C Called trimorphic numbers.

%C Corresponding values of n: 1, 5, 25, 625, 9376, 90625, 890625, 7109376, 12890625, 212890625, 1787109376, 81787109376, 59918212890625. - _Zak Seidov_, Apr 12 2013

%D James J. Tattersall, Elementary Number Theory in Nine Chapters, Second Edition, Cambridge University Press, p. 44, problem no. 9.

%e 15 is in the list since 15 = 5th triangular number and last digit of 15 is 5. Similarly 325 = 25th triangular number and last two digits of 325 gives 25.

%t t = {}; Do[k = n*(n + 1)/2; p = Length[IntegerDigits[n]]; If[FromDigits[Take[IntegerDigits[k], -p]] == n, AppendTo[t, k]], {n, 240000000}]; t

%K nonn,base

%O 1,2

%A _Jayanta Basu_, Apr 11 2013

%E a(11)-a(13) from _Zak Seidov_, Apr 12 2013