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

1,1

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A085305.

Sequence in context: A157884 A234530 A235632 * A161322 A123239 A048891

Adjacent sequences: A085303 A085304 A085305 * A085307 A085308 A085309

Keyword

base,nonn

Author

Labos Elemer, Jun 27 2003

Status

approved