A085306 Prime numbers such that first reversing digits and after squaring equals the result of first-squaring and after-reversing. Primes in A085305.

2, 3, 11, 13, 31, 101, 103, 113, 211, 311, 1013, 1021, 1031, 1103, 1201, 1301, 2011, 2111, 3001, 3011, 10103, 10111, 10211, 11003, 11113, 12011, 12101, 13001, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 22111, 30011, 100003, 100103, 101021

Offset: 1

Author

Labos Elemer, Jun 27 2003

Keywords

• base
• nonn

Examples

			n=13 is here because 31^2 = 961 = rev(169) = rev(13^2) = rev(rev(31)^2).
65 solutions below 1000000.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A085305.

Programs

Mathematica

rt[x_] := tn[Reverse[IntegerDigits[x]]] Do[s=rt[n^2]; s1=rt[n]^2; If[Equal[s, s1]&& !Equal[Mod[n, 10], 0]&&PrimeQ[n], Print[n]], {n, 1, 1000000}]
(* Second program: *)
Select[Prime[Range[10^5]], IntegerReverse[#]^2 == IntegerReverse[#^2]&] (* Jean-François Alcover, Feb 13 2021 *)

Formula

Prime number solutions to rev(x^2) = rev(x)^2.