|
| |
|
|
A049296
|
|
First differences of A008364. Also first differences of reduced residue system (RRS) for 4th primorial number, A002110(4)=210.
|
|
6
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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 n-th 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.
|
|
|
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&]] (* From Harvey P. Dale, Jan 13 2012 *)
|
|
|
CROSSREFS
| Cf. A005867, A008364, A002110, A001223.
Sequence in context: A201278 A010175 A160136 * A169851 A161995 A069036
Adjacent sequences: A049293 A049294 A049295 * A049297 A049298 A049299
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
|
|
|
EXTENSIONS
| Corrected by Frederic Devaux, Feb 02 2007
|
| |
|
|
