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Emirps p such that p plus its decimal reversal is a perfect square.
1

%I #66 Apr 03 2023 10:36:13

%S 303593,333563,336263,342653,344453,348053,350843,354443,356243,

%T 362633,365333,395303,744377,754367,755267,762557,763457,773447,

%U 3014393,3204473,3214373,3444053,3504443,3734123,3744023,3934103,79099019,91099097,100771943,101078843

%N Emirps p such that p plus its decimal reversal is a perfect square.

%C 303593 is the smallest emirp to satisfy the requirement.

%H Shyam Sunder Gupta, <a href="/A227780/b227780.txt">Table of n, a(n) for n = 1..310</a>

%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php/303593.html">Prime Curios! 303593</a>

%e a(1) = 303593: Reversing the digits gives 395303 and 303593 + 395303 = 698896 = 836^2.

%t t = {}; Do[n = Prime[x]; m = FromDigits[Reverse[IntegerDigits[Prime[x]]]]; If[IntegerQ[(n + m)^(1/2)] && PrimeQ[m] && m!=n, AppendTo[t, n]], {x, 1, 7000000}]; t

%Y Cf. A006567, A059799.

%K nonn,base

%O 1,1

%A _Shyam Sunder Gupta_, Aug 17 2013