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A008509
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Positive integers k such that k-th triangular number is palindromic.
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17
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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
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1
(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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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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