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