

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000


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
 Reinhard Zumkeller, Jan 06 2013


CROSSREFS

Cf. A005867, A008364, A002110, A001223.
Sequence in context: A306321 A160136 A322467 * A220468 A169851 A161995
Adjacent sequences: A049293 A049294 A049295 * A049297 A049298 A049299


KEYWORD

nonn,easy,nice


AUTHOR

Labos Elemer


EXTENSIONS

Corrected by Frederic Devaux, Feb 02 2007


STATUS

approved



