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A333854 Numbers 2*k + 1 with A135303(k) = 1, for k >= 1, sorted increasingly. 4

%I

%S 3,5,7,9,11,13,15,19,21,23,25,27,29,35,37,39,45,47,49,53,55,59,61,67,

%T 69,71,75,77,79,81,83,87,95,101,103,107,111,115,121,125,131,135,139,

%U 141,143,147,149,159,163,167,169,173,175,179,181,183,191,197,199,203

%N Numbers 2*k + 1 with A135303(k) = 1, for k >= 1, sorted increasingly.

%C These are the numbers a(n) for which there is only one periodic Schick sequence. In Schick's notation B(a(n)) = 1, for n >= 1.

%C These are the numbers a(n) for which there is only one coach in the complete coach system Sigma(b = a(n)) of Hilton and Pedersen, for n >= 1.

%C These are also the numbers a(n) for which there is only one cycle in the complete system MDS(a(n)) (Modified Doubling Sequence) proposed in the comment by _Gary W. Adamson_, Aug 20 2019, in A003558.

%C The subsequence of prime numbers is A216371.

%C The complement relative to the odd numbers >= 3 is given in A333855.

%D Peter Hilton and Jean Pedersen, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics, Cambridge University Press, 2010, pp. 261-264.

%D Carl Schick, Trigonometrie und unterhaltsame Zahlentheorie, Bokos Druck, Z├╝rich, 2003 (ISBN 3-9522917-0-6). Tables 3.1 to 3.10, for odd p = 3..113 (with gaps), pp. 158-166.

%F Sequence {a(n)}_{n >= 1} of numbers 2*k + 1 satisfying A135303(k) = 1, for k >= 1, ordered increasingly.

%o (PARI) isok8(m, n) = my(md = Mod(2, 2*n+1)^m); (md==1) || (md==-1);

%o A003558(n) = my(m=1); while(!isok8(m, n) , m++); m;

%o isok(m) = (m%2) && eulerphi(m)/(2*A003558((m-1)/2)) == 1; \\ _Michel Marcus_, Jun 10 2020

%Y Cf. A003558, A135303, A216371, A268923, A333855.

%K nonn

%O 1,1

%A _Wolfdieter Lang_, May 03 2020

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Last modified July 27 23:16 EDT 2021. Contains 346316 sequences. (Running on oeis4.)