

A002781


Palindromic cubes.
(Formerly M4583 N1954)


7



0, 1, 8, 343, 1331, 1030301, 1367631, 1003003001, 10662526601, 1000300030001, 1030607060301, 1334996994331, 1000030000300001, 1033394994933301, 1331399339931331, 1000003000003000001, 1003006007006003001, 1331039930399301331
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OFFSET

1,3


COMMENTS

a(9) = 1066252601 = 2201^3 is the unique known palindromic cube that has a nonpalindromic rootnumber (see comments in A002780 and Penguin reference).  Bernard Schott, Oct 21 2021


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised Edition), Penguin Books, 1997, entry 10662526601, page 188.


LINKS

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 9398. [Annotated scanned copy]


FORMULA



MATHEMATICA

Select[Range[0, 12*10^5]^3, PalindromeQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 02 2017 *)


PROG

(PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d); \\ A002113
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


CROSSREFS



KEYWORD

base,nonn,nice


AUTHOR



EXTENSIONS

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.


STATUS

approved



