OFFSET
1,3
COMMENTS
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
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
T. D. Noe, Table of n, a(n) for n = 1..89 (from De Geest)
Patrick De Geest, Palindromic Cubes
G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
G. J. Simmons, Palindrome cubes: Problem B-183, Fibonacci Quart. 8 (1970), no. 5, p. 551.
FORMULA
a(n) = A002780(n)^3.
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