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

1,1

Comments

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

Links

Table of n, a(n) for n=1..66.

Example

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

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

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

Crossrefs

Sequence in context: A115335 A214062 A054586 * A214728 A112752 A101035

Adjacent sequences: A214226 A214227 A214228 * A214230 A214231 A214232

Keyword

nonn

Author

Kenneth J Ramsey, Jul 07 2012

Status

approved