

A049296


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


9



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, 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, 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
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OFFSET

1,1


COMMENTS

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 nth primorial number.
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.
Difference sequence of the "4th diatomic sequence"  A. de Polignac (1849), J. Dechamps (1907).


REFERENCES

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


LINKS



MATHEMATICA

t1=Table[ GCD[ w, 210 ], {w, 1, 210} ] /t2=Flatten[ Position[ t1, 1 ] ] /t3=Mod[ RotateLeft[ t2 ]t2, 210 ]
Differences[Select[Range[600], GCD[#, 210]==1&]] (* Harvey P. Dale, Jan 13 2012 *)


PROG

(Haskell)
a049296 n = a049296_list !! (n1)
a049296_list = zipWith () (tail a008364_list) a008364_list


CROSSREFS



KEYWORD

nonn,easy,nice


AUTHOR



EXTENSIONS

Corrected by Frederic Devaux, Feb 02 2007


STATUS

approved



