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First differences of A008364. Also first differences of reduced residue system (RRS) for 4th primorial number, A002110(4)=210.
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%I #24 Apr 06 2014 08:13:30

%S 10,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,

%T 6,6,4,2,4,6,2,6,4,2,4,2,10,2,10,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,

%U 6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10,2,4,2,4,6,2

%N First differences of A008364. Also first differences of reduced residue system (RRS) for 4th primorial number, A002110(4)=210.

%C First differences of reduced residue systems modulo primorial numbers are essentially palindromic + 1 separator term (2). The palindromic part starts and ends with p_(n+1)-1 for the n-th primorial number.

%C This sequence has period A005867(4)=A000010(A002110(4))=48. The 0th, first, 2nd and 3rd similar difference sequences are as follows: {1},{2},{4,2},{6,4,2,4,2,4,6,2} obtained from reduced residue systems of consecutive primorials.

%C Difference sequence of the "4th diatomic sequence" - A. de Polignac (1849), J. Dechamps (1907).

%D Dickson L. E., History of the Theory of Numbers, Vol. 1, p. 439, Chelsea, 1952.

%H Reinhard Zumkeller, <a href="/A049296/b049296.txt">Table of n, a(n) for n = 1..1000</a>

%t t1=Table[ GCD[ w, 210 ], {w, 1, 210} ] /t2=Flatten[ Position[ t1, 1 ] ] /t3=Mod[ RotateLeft[ t2 ]-t2, 210 ]

%t Differences[Select[Range[600],GCD[#,210]==1&]] (* _Harvey P. Dale_, Jan 13 2012 *)

%o (Haskell)

%o a049296 n = a049296_list !! (n-1)

%o a049296_list = zipWith (-) (tail a008364_list) a008364_list

%o -- _Reinhard Zumkeller_, Jan 06 2013

%Y Cf. A005867, A008364, A002110, A001223.

%K nonn,easy,nice

%O 1,1

%A _Labos Elemer_

%E Corrected by Frederic Devaux, Feb 02 2007