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%I M4583 N1954 #34 May 21 2022 14:49:08
%S 0,1,8,343,1331,1030301,1367631,1003003001,10662526601,1000300030001,
%T 1030607060301,1334996994331,1000030000300001,1033394994933301,
%U 1331399339931331,1000003000003000001,1003006007006003001,1331039930399301331
%N Palindromic cubes.
%C a(9) = 1066252601 = 2201^3 is the unique known palindromic cube that has a non-palindromic rootnumber (see comments in A002780 and Penguin reference). - _Bernard Schott_, Oct 21 2021
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised Edition), Penguin Books, 1997, entry 10662526601, page 188.
%H T. D. Noe, <a href="/A002781/b002781.txt">Table of n, a(n) for n = 1..89</a> (from De Geest)
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/cube.htm">Palindromic Cubes</a>
%H G. J. Simmons, <a href="/A002778/a002778_2.pdf">Palindromic powers</a>, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
%H G. J. Simmons, <a href="/A002778/a002778.pdf">On palindromic squares of non-palindromic numbers</a>, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
%H G. J. Simmons, <a href="https://www.fq.math.ca/Scanned/8-5/elementary8-5.pdf">Palindrome cubes: Problem B-183</a>, Fibonacci Quart. 8 (1970), no. 5, p. 551.
%F a(n) = A002780(n)^3.
%t Select[Range[0,12*10^5]^3,PalindromeQ[#]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 02 2017 *)
%o (PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d); \\ A002113
%o lista(nn) = my(list = List(), c); for (n=0, sqrtnint(nn, 3), if (ispal(c=n^3), listput(list, c));); Vec(list); \\ _Michel Marcus_, Oct 21 2021
%Y Cf. A002780.
%Y Intersection of A000578 and A002113.
%K base,nonn,nice
%O 1,3
%A _N. J. A. Sloane_
%E Thanks to Pierre Genix (Pierre.Genix(AT)wanadoo.fr) and _Harvey P. Dale_ who pointed out that there were errors in earlier versions of this sequence.
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