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A003098
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Palindromic triangular numbers.
(Formerly M2605)
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28
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0, 1, 3, 6, 55, 66, 171, 595, 666, 3003, 5995, 8778, 15051, 66066, 617716, 828828, 1269621, 1680861, 3544453, 5073705, 5676765, 6295926, 35133153, 61477416, 178727871, 1264114621, 1634004361, 5289009825, 6172882716, 13953435931
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OFFSET
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1,3
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 73 and p. 178, entry 828828 (Rev. ed. 1997)
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LINKS
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MATHEMATICA
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palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; Select[ Accumulate[ Range[200000]], palQ] (* Harvey P. Dale, Mar 23 2011 *)
Select[Accumulate[Range[0, 170000]], PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 15 2019 *)
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PROG
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(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
(Python)
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
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CROSSREFS
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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STATUS
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approved
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