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%I #42 Jan 02 2023 12:30:46
%S 0,1,2,7,11,101,111,1001,10001,10101,11011,100001,101101,110011,
%T 1000001,1001001,1100011,10000001,10011001,10100101,11000011,
%U 100000001,100010001,100101001,101000101,110000011,1000000001,1000110001,1010000101,1100000011,10000000001
%N Numbers k such that k and k^3 are both palindromes.
%C 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.
%C Perhaps this sequence is the same as A002780, except for 2201. - _Dmitry Kamenetsky_, Apr 16 2009
%C 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
%H Michael S. Branicky, <a href="/A069748/b069748.txt">Table of n, a(n) for n = 1..117</a>
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2011-May/007522.html">Re: numbers whose cube is a palindrome</a>, seqfan list, May 25 2011
%t isPalin[n_] := (n == FromDigits[Reverse[IntegerDigits[n]]]); Do[m = n^3; If[isPalin[n] && isPalin[m], Print[{n, m}]], {n, 1, 10^6}]
%o (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d);
%o isok(n) = ispal(n) && ispal(n^3); \\ _Michel Marcus_, Dec 16 2018
%Y Intersection of A002113 and A002780.
%K base,nonn
%O 1,3
%A _Joseph L. Pe_, Apr 22 2002
%E a(29) and beyond from _Michael S. Branicky_, Aug 06 2022