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A214229 a(n) equals GCD(r,2*n+1) where r is 1 + (A143608(i+1) modulus (2*n+1)) where A143608(i) is the first zero mod 2n+1 other than 0. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)