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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 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.)