A247585 Period of the decimal expansion of 1/p as p runs through the prime numbers of the form n^2+1 (0 by convention for the primes 2 and 5).

0, 0, 16, 3, 4, 98, 256, 200, 576, 338, 1296, 200, 1458, 3136, 242, 1369, 7056, 1620, 4418, 12100, 13456, 3600, 15376, 567, 3380, 8978, 10658, 7500, 24336, 25, 5780, 30976, 600, 33856, 41616, 10609, 44100, 50176, 52900, 55696, 14400, 62500, 65536, 33800, 69696, 8100

Offset: 1

Author

Michel Lagneau, Sep 20 2014

Keywords

• nonn

Comments

Subsequence of A002371 or period of the decimal expansion of 1/A002496(n).

The squares > 0 in the sequence are 4, 16, 25, 256, 576, 1296, 1369, 3136, 3600, 7056, 8100, 10609, ...

Examples

			a(3) = 16 because A002496(3) = 17 and 1/17 = 0. 0588235294117647 0588235294117647 ... has period 16.
		

Crossrefs

Cf. A000720, A002371, A002496, A060282, A175550.

Programs

Mathematica

lst={};Do[If[PrimeQ[n^2+1],AppendTo[lst,n^2+1]],{n,1,1000}];Table[Length[RealDigits[1/lst[[m]]][[1,1]]],{m,1,60}]

Formula

a(n) = A002371(A000720(A002496(n))). [Corrected by Georg Fischer, Oct 19 2024]