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%I #24 Feb 26 2022 04:23:46
%S 65,5625,6565,50721,65065,71555,75515,84295,541063,557931,650065,
%T 650606,656565,699796,809325,827372,934065,2855182,4637061,4854634,
%U 5791775,5883141,5951693,6129084,6500065,6731076,6752626,6791774,7768827,8084505,9349065
%N Nonpalindromic numbers m such that the difference between the square of m and the square of the reversal of m is itself a perfect square. Numbers ending in 0 are excluded.
%C This sequence is infinite because 65*10^k + 65 is a term for all k > 1.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 147.
%H Giovanni Resta, <a href="/A202386/b202386.txt">Table of n, a(n) for n = 1..200</a>
%H Sheng Jiang and Rui-Chen Chen, <a href="https://doi.org/10.1080/0020739980290505">Digits reversed Pythagorean triples</a>, International Journal of Mathematical Education in Science and Technology, volume 29, number 5, 1998, pages 689-696, see type acca-DRPT.
%e 5625 belongs to this sequence because 5625^2 - 5265^2 = 1980^2.
%t lst = {}; Do[a = n^2; b = FromDigits[Reverse[IntegerDigits[n]]]^2; If[MatchQ[Sqrt[a - b], _Integer] && ! a == b, AppendTo[lst, n]], {n, 85000}]; Select[lst, ! Mod[#, 10] == 0 &]
%o (PARI) isok(m) = my(r=fromdigits(Vecrev(digits(m)))); (r != m) && (m % 10) && issquare(m^2 - r^2); \\ _Michel Marcus_, Feb 27 2020
%Y Cf. A000290 (squares), A004086 (digit reversal).
%Y Cf. A256515 (with abs), A068536 (with addition).
%K nonn,base
%O 1,1
%A _Arkadiusz Wesolowski_, Dec 18 2011
%E Name clarified by _Michel Marcus_, Feb 27 2020
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