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Ratios (p-1)/d, where p is a prime and d is the number of digits of the periodic part of the decimal expansion of 1/p.
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%I #13 Mar 16 2022 20:00:01

%S 1,2,4,1,5,2,1,1,1,1,2,12,8,2,1,4,1,1,2,2,9,6,2,2,1,25,3,2,1,1,3,1,17,

%T 3,1,2,2,2,1,4,1,1,2,1,2,2,7,1,2,1,1,34,8,5,1,1,1,54,4,10,2,2,2,2,1,4,

%U 3,1,2,3,11,2,1,2,1,1,1,4,2,2,1,3,2,1,2

%N Ratios (p-1)/d, where p is a prime and d is the number of digits of the periodic part of the decimal expansion of 1/p.

%C The sequence of 2nd, 4th and following terms coincides with A006556, which gives the "number of different cycles of digits in the decimal expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2 or 5".

%H Carmine Suriano and T. D. Noe, <a href="/A060370/b060370.txt">Table of n, a(n) for n = 1..10000</a> (first 101 terms from Carmine Suriano)

%F a(n) = (b(n)-1)/c(n), where b(n) and c(n) are the n-th terms of A000040 and A048595 respectively.

%e a(13) = 40/5 = 8, since 41 is the 13th prime and the periodic part of 1/41 = 0.02439024390... consists of 5 digits.

%t Join[{1, 2, 4}, Table[p = Prime[n]; (p - 1)/Length[RealDigits[1/p, 10][[1, 1]]], {n, 4, 100}]] (* _T. D. Noe_, Oct 04 2012 *)

%o (Python) from sympy import prime, n_order

%o def A060370(n): return 1 if n == 1 or n == 3 else n_order(10, prime(n))

%o print([(prime(n)-1)//A060370(n) for n in range(1,86)]) # _Karl-Heinz Hofmann_, Mar 16 2022

%Y Cf. A000040, A060283, A048595, A006556.

%K nonn,base

%O 1,2

%A _Klaus Brockhaus_, Apr 01 2001