A072858 Primes p such that the period of the decimal expansion of 1/p is a square.

2, 3, 5, 17, 101, 163, 257, 577, 883, 1297, 1801, 3137, 3529, 5477, 7057, 7351, 8929, 9397, 11831, 12101, 13457, 13553, 14401, 15361, 15377, 15973, 19841, 20809, 21401, 21601, 23549, 24337, 25601, 29401, 30977, 33301, 33751, 33857, 38237

Offset: 1

Author

Benoit Cloitre, Jul 26 2002

Keywords

• easy
• nonn
• base

Examples

			The period of 1/17 = 0.05882352941176470588... is 16 = 4^2, hence 17 is in the sequence.
The period of 1/163 = 81 = 9^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002371.

Programs

Mathematica

Select[Prime[Range[4000]], IntegerQ @ Sqrt[Length[RealDigits[1/#][[1, 1]]]] &] (* Amiram Eldar, May 21 2022 *)

PARI

(a(n)=if(n<4,n==2,znorder(Mod(10, prime(n))))); for(n=1,1000,if(issquare(a(n))==1,print1(prime(n),","))) /* Thanks to Michael Somos for improvement of the PARI program */