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A202386 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. 5

%I

%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>

%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. A068536, A000290.

%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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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)