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

Author

Patrick De Geest

Keywords

• nonn
• base
• more

References

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

Links

• 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.

Programs

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 *)