login
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, 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, ...
FORMULA
a(n) = A002371(A000720(A002496(n))). [Corrected by Georg Fischer, Oct 19 2024]
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 20 2014
STATUS
approved