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A214229 a(n) equals gcd(r,2*n+1) where r is 1 + (A143608(i+1) mod (2*n+1)) where A143608(i) is the first zero mod 2n+1 other than 0. 1

%I

%S 3,5,1,9,11,13,3,17,19,3,1,25,27,29,1,33,5,37,3,1,43,9,1,1,17,53,11,

%T 57,59,61,9,65,67,3,1,73,3,11,1,81,83,17,3,89,13,3,19,97,99,101,1,3,

%U 107,109,3,113,5,9,17,121,3,125,1,129,131,19

%N a(n) equals gcd(r,2*n+1) where r is 1 + (A143608(i+1) mod (2*n+1)) where A143608(i) is the first zero mod 2n+1 other than 0.

%C It appears that a(n) * b(n) either equals 2*n+1 or 1 where b is the companion sequence A214228.

%e a(7) = 3 which is a factor of 2*7 + 1.

%p A214229 := proc(n)

%p local i,r ;

%p i := 1;

%p while A143608(i) mod (2*n+1) <> 0 do

%p i := i+1 ;

%p end do;

%p r := 1+(A143608(i+1) mod (2*n+1)) ;

%p gcd(r,2*n+1) ;

%p end proc: # _R. J. Mathar_, Jul 22 2012

%t gcdN2[x_,y_] = GCD[y - x + 1,y];

%t r0 = 3;

%t table=Reap[While[r0 < 200,s1=1;s0=0;count=1;While[True,count++;temp=Mod[4*s1 - s0,r0];

%t If[temp==0,Break[]];count++;s0 = s1; s1 = temp;

%t temp=Mod[2*s1-s0,r0];If[temp == 0,Break[]];s0 = s1;s1 = temp;];

%t Sow[gcdN2[s1,r0],d];

%t r0+=2;]][[2]];

%t table

%K nonn

%O 1,1

%A _Kenneth J Ramsey_, Jul 07 2012

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Last modified August 14 23:38 EDT 2022. Contains 356122 sequences. (Running on oeis4.)