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A062936 Numbers n such that n*R(n) is a palindrome, where R(n) (A004086) = digit reversal.

%I A062936 #53 Mar 04 2025 15:20:48
%S A062936 1,2,3,11,12,21,22,101,102,111,112,121,122,201,202,211,212,221,1001,
%T A062936 1002,1011,1012,1021,1022,1101,1102,1111,1112,1121,1201,1202,1211,
%U A062936 2001,2002,2011,2012,2021,2101,2102,2111,2201,10001,10002,10011,10012
%N A062936 Numbers n such that n*R(n) is a palindrome, where R(n) (A004086) = digit reversal.
%H A062936 Harry J. Smith and Indranil Ghosh, <a href="/A062936/b062936.txt">Table of n, a(n) for n = 1..4357</a> (first 500 terms from Harry J. Smith)
%H A062936 Martianus Frederic Ezerman, Bertrand Meyer and Patrick Solé, <a href="http://arxiv.org/abs/1210.7593">On Polynomial Pairs of Integers</a>, arXiv:1210.7593 [math.NT], 2012. - From _N. J. A. Sloane_, Nov 08 2012
%H A062936 Martianus Frederic Ezerman, Bertrand Meyer and Patrick Solé, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Ezerman/eze3.html">On Polynomial Pairs of Integers</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.5.
%F A062936 Includes integers not ending in 0 with sum of squares of digits < 10. - _David W. Wilson_, Jul 06 2001
%e A062936 122*221 = 26962 hence 122 belongs to the sequence.
%t A062936 Select[Range[100000], Reverse[IntegerDigits[ #*FromDigits[Reverse[IntegerDigits[ # ]]]]] == IntegerDigits[ #*FromDigits[Reverse[IntegerDigits[ # ]]]] &] (* _Tanya Khovanova_, Jun 17 2009 *)
%t A062936 Select[Range[11000],PalindromeQ[# IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 21 2020 *)
%o A062936 (PARI) lista(nn) = for(n=1, nn, my(d=digits(n*eval(concat(Vecrev(Str(n)))), 10)); if(d == Vecrev(d), print1(n, ", "))); \\ _Altug Alkan_, Mar 26 2016
%o A062936 (Python)
%o A062936 A062936_list = []
%o A062936 for n in range(1,10**5):
%o A062936     s = str(n*int(str(n)[::-1]))
%o A062936     if s == s[::-1]:
%o A062936         A062936_list.append(n) # _Chai Wah Wu_, Sep 08 2014
%Y A062936 Cf. A048343, A048344.
%K A062936 nonn,base,easy
%O A062936 1,2
%A A062936 _Amarnath Murthy_, Jul 05 2001
%E A062936 Corrected and extended by _Dean Hickerson_ and _Patrick De Geest_, Jul 06 2001