A279084 Numbers k such that reverse(T(k)) = T(reverse(k)) where T(k) is the k-th triangular number.

0, 1, 2, 3, 11, 77, 363, 1111, 2662, 24662, 26642, 111111, 246642, 11111111, 363474363, 2664444662

Offset

1,3

Comments

The k-th triangular number is T(k) = k*(k+1)/2 = A000217(k).

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.

If it exists, a(17) > 10^12. - Lars Blomberg, Jan 23 2017

Links

Table of n, a(n) for n=1..16.

Example

Since reverse(T(11)) = reverse(66) = 66 = T(11) = T(reverse(11)), 11 is in the sequence.
Since reverse(T(24662)) = reverse(304119453) = 354911403 = T(26642) = T(reverse(24662)), 24662 is in the sequence (and so is its reverse, 26642).

Prog

(PARI) rev(n) = eval(concat(Vecrev(Str(n))));
trg(n) = n*(n+1)/2;
isok(n) = rev(trg(n)) == trg(rev(n)); \\ Michel Marcus, Jan 14 2017

Crossrefs

Cf. A000217, A008510.

Sequence in context: A155187 A338613 A109132 * A008510 A290512 A042165

Adjacent sequences: A279081 A279082 A279083 * A279085 A279086 A279087

Keyword

nonn,base,more

Author

Jon E. Schoenfield, Jan 14 2017

Extensions

a(16) from Lars Blomberg, Jan 23 2017

Status

approved