OFFSET
1,3
COMMENTS
For an arithmetical function f, call the pairs (x,y) such that y = f(x) and x, y are palindromes the "palinpairs" of f. {a(n)} is then the sequence of abscissae of palinpairs of f(n) = n^3.
Perhaps this sequence is the same as A002780, except for 2201. - Dmitry Kamenetsky, Apr 16 2009
For n >= 5, there are no terms with digit sum 5. Conjecture: all terms belong to one of 3 disjoint classes of the following forms: 10^k+1, 10^(2*t)+10^t+1, t > 0, and (10^u+1)*(10^v+1), u,v > 0, with digit sums 2, 3 and 4 correspondingly. - Vladimir Shevelev, May 31 2011
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..117
Vladimir Shevelev, Re: numbers whose cube is a palindrome, seqfan list, May 25 2011
MATHEMATICA
isPalin[n_] := (n == FromDigits[Reverse[IntegerDigits[n]]]); Do[m = n^3; If[isPalin[n] && isPalin[m], Print[{n, m}]], {n, 1, 10^6}]
PROG
(PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(n) = ispal(n) && ispal(n^3); \\ Michel Marcus, Dec 16 2018
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Joseph L. Pe, Apr 22 2002
EXTENSIONS
a(29) and beyond from Michael S. Branicky, Aug 06 2022
STATUS
approved