A008509 Positive integers k such that k-th triangular number is palindromic.

1, 2, 3, 10, 11, 18, 34, 36, 77, 109, 132, 173, 363, 1111, 1287, 1593, 1833, 2662, 3185, 3369, 3548, 8382, 11088, 18906, 50281, 57166, 102849, 111111, 167053, 179158, 246642, 337650, 342270, 365436, 417972, 1620621, 3240425, 3457634, 3707883

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

References

• Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
• D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 93.

Links

• T. D. Noe, Table of n, a(n) for n = 1..147 (from P. De Geest)
• P. De Geest, Palindromic Triangulars

Crossrefs

Cf. A003098, A002113, A000217, A083571, A050721, A050722.

Programs

Magma

[k:k in [1..5000000]| Intseq(Binomial(k+1,2)) eq Reverse(Intseq(Binomial(k+1,2)))]; //  Marius A. Burtea, Jul 16 2019

Mathematica

palQ[n_]:= Reverse[x=IntegerDigits[n]]==x; t={}; Do[If[palQ[n*(n+1)/2],AppendTo[t,n]],{n,4*10^6}]; t (* Jayanta Basu, May 13 2013 *)
Position[Accumulate[Range[371*10^4]],?PalindromeQ]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Jun 12 2020 *)

PARI

ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1
is(n)=ispal(n*(n+1)/2) \\ Charles R Greathouse IV, May 15 2013