A002781 Palindromic cubes.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• nonn
• nice

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.

Crossrefs

Cf. A002780.

Intersection of A000578 and A002113.

Programs

Mathematica

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

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

Formula

a(n) = A002780(n)^3.

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.