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 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

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