A087988 Palindromic numbers whose squares and cubes are equally palindromic.

0, 1, 2, 11, 101, 111, 1001, 10001, 10101, 11011, 100001, 101101, 110011, 1000001, 1001001, 1100011, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 1000000001, 1000110001

Offset: 1

Author

Labos Elemer, Oct 01 2003

Keywords

• nonn
• base

Comments

Numbers n such that n, n^2 and n^3 are all palindromes.

Essentially A002780 with two terms removed, 7 and 2201.

Examples

			11^2=121, 11^3=1331.
		

Crossrefs

Cf. A002779, A002781.

Intersection of A002113, A002778 and A002780.

Programs

Maple

rev:=proc(a) local aa,ct: aa:=convert(a,base,10): ct:=nops(aa): add(10^(ct-j)*aa[j],j=1..ct) end: p:=proc(n) if rev(n)=n and rev(n^2)=n^2 and rev(n^3)=n^3 then n else fi end: seq(p(n),n=0..12*10^5); # Emeric Deutsch, May 01 2005

PARI

ispal(n) = my(d = digits(n)); Vecrev(d) == d;
isok(n) = ispal(n) && ispal(n^2) && ispal(n^3); \\ Michel Marcus, Oct 25 2015

Extensions

More terms from Ray Chandler, Oct 05 2003

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar