login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A200143 Nodes of degree 1 in graphs of XOR connected primes in successive intervals [2^i+1,2^(i+1)-1], i>=1. 2
5, 7, 11, 13, 23, 47, 61, 83, 131, 191, 211, 223, 241, 317, 331, 397, 467, 479, 491, 503, 509, 563, 577, 613, 727, 743, 757, 829, 887, 907, 941, 947, 997, 1009, 1021, 1039, 1069, 1087, 1097, 1109, 1223, 1229, 1237, 1381, 1399, 1423, 1447, 1523, 1543, 1549 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number used to produce the XOR couple is 2^i-2, with i sharing the index value of the initial interval and decremented in halved intervals down to 2.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

In the interval [17,31], i=4, the XOR couple number is 2^4-2=14. For half intervals it is 2^3-2 = 6, and the final application would be 2^2-2 = 2. All of the pairings can be represented as:

|-------XOR 14-------|

|  |--------------|  |

|  |  |--------|  |  |

|  |  |  |--|  |  |  |

17 19 21 23 25 27 29 31

|-XOR  6-|  |-XOR  6-|

|  |--|  |  |  |--|  |

17 19 21 23 25 27 29 31

XOR   XOR   XOR   XOR

|2-|  |2-|  |2-|  |2-|

17 19 21 23 25 27 29 31

The prime XOR couples are (17,31), (19,29), (17,23), (17,19), (29,31) which produces the graph:

  17 19 23 29 31

17 0  1  1  0  1             19

19 1  0  0  1  0           /    \

23 1  0  0  0  0   or  23~17~31~29

29 0  1  0  0  1

31 1  0  0  1  0

Therefore 23 is the only node of degree 1 in the interval.

MAPLE

q:= (l, p, r)-> `if`(r-l=2, 0, `if`(isprime(l+r-p), 1, 0)+

                `if`((l+r)/2>p, q(l, p, (l+r)/2), q((l+r)/2, p, r))):

a:= proc(n) local p, l;

      p:= `if`(n=1, 1, a(n-1));

      do p:= nextprime(p);

         l:= 2^ilog2(p);

         if q(l, p, l+l)=1 then break fi

      od; a(n):=p

    end:

seq(a(n), n=1..60);  # Alois P. Heinz, Nov 15 2011

CROSSREFS

Cf. A199824.

Sequence in context: A022885 A176831 A263467 * A265780 A135774 A180946

Adjacent sequences:  A200140 A200141 A200142 * A200144 A200145 A200146

KEYWORD

nonn

AUTHOR

Brad Clardy, Nov 14 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 09:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)