A214228 - OEIS

%I #29 Aug 02 2019 03:43:40

%S 1,1,1,1,1,1,5,1,1,7,1,1,1,1,1,1,7,1,13,1,1,5,1,1,3,1,5,1,1,1,7,1,1,

%T 23,1,1,25,7,1,1,1,5,29,1,7,31,5,1,1,1,1,35,1,1,37,1,23,13,7,1,41,1,1,

%U 1,1,7,5,1,1,47,13,1,49,1,1,9,31,1,53

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

%C It appears that a(n) * gcd(s,2*n+1) is either 2*n+1 or 1; where s is 1 + (A143608(i+1) mod (2*n+1)) and A143608(i) is as stated in the definition.

%e a(7) = 5 which is a factor of 2*7+1.

%p A214228 := 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 gcdN1[x_,y_] = GCD[x + 1,y]; r0 = 3; Reap[While[r0 < 200, s1=1; s0=0; count=1; While[True, count++; temp=Mod[4*s1 - s0, r0]; If[temp==0, Break[]]; count++; s0 = s1; s1 = temp; temp=Mod[2*s1-s0,r0]; If[temp == 0, Break[]]; s0 = s1; s1 = temp;]; Sow[gcdN1[s1, r0], c]; r0+=2;]][[2,1]]

%Y Cf. A143608.

%K nonn

%O 1,7

%A _Kenneth J Ramsey_, Jul 07 2012