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

1,2

References

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

Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.

David 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)

Patrick De Geest, Palindromic Triangulars.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A248407 A047473 A270474 * A281366 A324921 A307034

Adjacent sequences: A008506 A008507 A008508 * A008510 A008511 A008512

Keyword

nonn,base

Author

Patrick De Geest

Status

approved