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%I #19 Jan 23 2017 10:01:16
%S 0,1,2,3,11,77,363,1111,2662,24662,26642,111111,246642,11111111,
%T 363474363,2664444662
%N Numbers k such that reverse(T(k)) = T(reverse(k)) where T(k) is the k-th triangular number.
%C The k-th triangular number is T(k) = k*(k+1)/2 = A000217(k).
%C This sequence includes all numbers k such that both k and T(k) are palindromes (A008510); it also includes at least one pair of nonpalindromes (see Example section). It includes 11, 1111, 111111, and 11111111, but not 1111111111.
%C If it exists, a(17) > 10^12. - _Lars Blomberg_, Jan 23 2017
%e Since reverse(T(11)) = reverse(66) = 66 = T(11) = T(reverse(11)), 11 is in the sequence.
%e Since reverse(T(24662)) = reverse(304119453) = 354911403 = T(26642) = T(reverse(24662)), 24662 is in the sequence (and so is its reverse, 26642).
%o (PARI) rev(n) = eval(concat(Vecrev(Str(n))));
%o trg(n) = n*(n+1)/2;
%o isok(n) = rev(trg(n)) == trg(rev(n)); \\ _Michel Marcus_, Jan 14 2017
%Y Cf. A000217, A008510.
%K nonn,base,more
%O 1,3
%A _Jon E. Schoenfield_, Jan 14 2017
%E a(16) from _Lars Blomberg_, Jan 23 2017