A008510 Numbers k such that both k and the k-th triangular number are palindromes.

1, 2, 3, 11, 77, 363, 1111, 2662, 111111, 246642, 11111111, 363474363, 2664444662, 26644444662, 246644446642, 266444444662, 2466444446642, 3654345456545434563

Offset

1,2

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 278.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 93.

Links

Table of n, a(n) for n=1..18.

Patrick De Geest, Subsets of palindromic triangulars.

Patrick De Geest, For the last term.

Shyam Sunder Gupta, Triangular Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 83-125.

Mathematica

palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {}; Do[If[palQ[n] && palQ[n*(n + 1)/2], AppendTo[t, n]], {n, 1.2*10^7}]; t (* Jayanta Basu, May 15 2013 *)

Crossrefs

Cf. A000217, A002113.

Sequence in context: A338613 A109132 A279084 * A290512 A042165 A395558

Adjacent sequences: A008507 A008508 A008509 * A008511 A008512 A008513

Keyword

nonn,base,more

Author

Patrick De Geest

Status

approved