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

1,3

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, ...

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = A002371(A002496(n)).

Example

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

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}]

Crossrefs

Cf. A002371, A002496, A060282, A175550.

Sequence in context: A040249 A099143 A070709 * A068615 A341720 A139722

Adjacent sequences: A247582 A247583 A247584 * A247586 A247587 A247588

Keyword

nonn

Author

Michel Lagneau, Sep 20 2014

Status

approved