0,3

For n>=9, a(n-1)+a(n-2) is even so a(n) is odd and >= 2n-1. It appears that a(n)=2n-1 infinitely often, when a(n-1)+a(n-2)=2p with p prime. A good upper bound is not known; presumably a(n)/n is unbounded, since it's large whenever a(n-1)+a(n-2) is divisible by many small primes. - Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 07 2006

Zak Seidov observed that straight lines are visible in the graph of a(n). The lowest line is given by the points with a(n)=2n-1. There are also many points a short distance above this line; these occur when a(n-1)+a(n-2) is a small power of 2 times a prime. Other lines show points with a(n-1)+a(n-2) equal to a small number times a large prime; e.g. when n>18 and a(n-1)+a(n-2)=6p, a(n) is either 3n+1 or 3n+2. - Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 07 2006

Zak Seidov, Table of n, a(n) for n = 0..999.

a(6)+a(7)=21. 1,2,4,5,8,10,11,13,16,17,... are the positive integers which are coprime to 21. 13 is the 8th of these integers, so a(8) = 13.

f[l_List] := Block[{k = 0, c = Length[l]}, While[c > 0, k++; While[GCD[k, l[[ -1]] + l[[ -2]]] > 1, k++ ]; c--; ]; Append[l, k]]; Nest[f, {0, 1}, 65] (*Chandler*)

a[0]=0; a[1]=1; a[n_]:=a[n]=Module[{s, c, v}, s=a[n-1]+a[n-2]; v=0; For[c=1, c<=n, c++, While[GCD[ ++v, s]>1, Null]]; v] (* Hickerson* )

Cf. A121047.

Sequence in context: A012722 A012616 A012611 this_sequence A075488 A136995 A136993

Adjacent sequences: A124180 A124181 A124182 this_sequence A124184 A124185 A124186

nonn

Leroy Quet (qq-quet(AT)mindspring.com), Dec 05 2006

Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Zak Seidov (zakseidov(AT)yahoo.com), Dec 06 2006