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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A002371.

Sequence in context: A308316 A089983 A370606 * A276629 A218086 A291049

Adjacent sequences: A072855 A072856 A072857 * A072859 A072860 A072861

Keyword

easy,nonn,base

Author

Benoit Cloitre, Jul 26 2002

Status

approved