A069748 Numbers k such that k and k^3 are both palindromes.

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, 1010000101, 1100000011, 10000000001

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

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

Extensions

a(29) and beyond from Michael S. Branicky, Aug 06 2022

Status

approved