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%I M2605 #50 Apr 29 2022 20:43:38
%S 0,1,3,6,55,66,171,595,666,3003,5995,8778,15051,66066,617716,828828,
%T 1269621,1680861,3544453,5073705,5676765,6295926,35133153,61477416,
%U 178727871,1264114621,1634004361,5289009825,6172882716,13953435931
%N Palindromic triangular numbers.
%C The only known terms with an even number 2*m of digits that are the concatenation of two palindromes with m digits are 55, 66 and 828828 (see David Wells entry 828828). - _Bernard Schott_, Apr 29 2022
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 73 and p. 178, entry 828828 (Rev. ed. 1997)
%H T. D. Noe, <a href="/A003098/b003098.txt">Table of n, a(n) for n = 1..148</a> (from Patrick De Geest)
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/triangle.htm">Palindromic Triangulars</a>
%t palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; Select[ Accumulate[ Range[200000]],palQ] (* _Harvey P. Dale_, Mar 23 2011 *)
%t Select[Accumulate[Range[0,170000]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 15 2019 *)
%o (PARI) list(lim)=my(v=List(),d); for(n=0,(sqrt(8*lim+1)-1)/2, d=digits(n*(n+1)/2); if(d==Vecrev(d), listput(v,n*(n+1)/2))); Vec(v) \\ _Charles R Greathouse IV_, Jun 23 2017
%o (Python)
%o A003098_list = [m for m in (n*(n+1)//2 for n in range(10**5)) if str(m) == str(m)[::-1]] # _Chai Wah Wu_, Sep 03 2021
%Y Cf. A008509.
%Y Intersection of A000217 and A002113.
%K nonn,base,easy,nice
%O 1,3
%A _N. J. A. Sloane_
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