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.
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, 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, 107, 109, 3, 113, 5, 9, 17, 121, 3, 125, 1, 129, 131, 19
Offset: 1
Keywords
Examples
a(7) = 3 which is a factor of 2*7 + 1.
Programs
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Maple
A214229 := proc(n) local i,r ; i := 1; while A143608(i) mod (2*n+1) <> 0 do i := i+1 ; end do; r := 1+(A143608(i+1) mod (2*n+1)) ; gcd(r,2*n+1) ; end proc: # R. J. Mathar, Jul 22 2012
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Mathematica
gcdN2[x_,y_] = GCD[y - x + 1,y]; r0 = 3; table=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[gcdN2[s1,r0],d]; r0+=2;]][[2]]; table
Comments