

A069748


Numbers n such that n and n^3 are both palindromes.


5



0, 1, 2, 7, 11, 101, 111, 1001, 10001, 10101, 11011, 100001, 101101, 110011, 1000001, 1001001, 1100011, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 1000000001, 1000110001
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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

Table of n, a(n) for n=1..28.
V. 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

Intersection of A002113 and A002780.
Sequence in context: A085315 A002780 A069885 * A064441 A110949 A226703
Adjacent sequences: A069745 A069746 A069747 * A069749 A069750 A069751


KEYWORD

base,nonn


AUTHOR

Joseph L. Pe, Apr 22 2002


STATUS

approved



