

A124183


a(0) = 0; a(1) = 1; for n >= 2, a(n) = the nth integer from among those positive integers which are coprime to a(n1)+a(n2).


1



0, 1, 2, 4, 11, 8, 6, 15, 13, 19, 19, 23, 41, 25, 43, 31, 31, 35, 59, 37, 59, 61, 79, 67, 47, 77, 53, 71, 57, 57, 91, 63, 81, 97, 67, 71, 109, 137, 115, 137, 139, 127, 103, 111, 87, 149, 93, 103, 111, 97, 107, 161, 105, 129, 175, 115, 143, 173, 117, 151, 121, 129, 153
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OFFSET

0,3


COMMENTS

For n>=9, a(n1)+a(n2) is even so a(n) is odd and >= 2n1. It appears that a(n)=2n1 infinitely often, when a(n1)+a(n2)=2p with p prime. A good upper bound is not known; presumably a(n)/n is unbounded, since it's large whenever a(n1)+a(n2) is divisible by many small primes.  Dean Hickerson, 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)=2n1. There are also many points a short distance above this line; these occur when a(n1)+a(n2) is a small power of 2 times a prime. Other lines show points with a(n1)+a(n2) equal to a small number times a large prime; e.g. when n>18 and a(n1)+a(n2)=6p, a(n) is either 3n+1 or 3n+2.  Dean Hickerson, Dec 07 2006


LINKS

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


EXAMPLE

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.


MATHEMATICA

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] (* Ray Chandler, Dec 06 2006 *)
a[0]=0; a[1]=1; a[n_]:=a[n]=Module[{s, c, v}, s=a[n1]+a[n2]; v=0; For[c=1, c<=n, c++, While[GCD[ ++v, s]>1, Null]]; v] (* _Hickerson_* )


CROSSREFS

Cf. A121047.
Sequence in context: A012616 A012611 A246164 * A218643 A300375 A075488
Adjacent sequences: A124180 A124181 A124182 * A124184 A124185 A124186


KEYWORD

nonn


AUTHOR

Leroy Quet, Dec 05 2006


EXTENSIONS

Extended by Ray Chandler and Zak Seidov, Dec 06 2006


STATUS

approved



