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A122457 a(1)=1, a(2)=1. a(n) = the sum of the two largest earlier terms which are both coprime to n. 2
1, 1, 2, 2, 4, 2, 6, 2, 6, 2, 12, 2, 18, 2, 6, 2, 30, 2, 48, 2, 6, 2, 78, 2, 126, 2, 6, 2, 204, 2, 330, 2, 6, 2, 282, 2, 612, 2, 6, 2, 942, 2, 1554, 2, 6, 2, 2496, 2, 3438, 2, 6, 2, 5934, 2, 9372, 2, 6, 2, 15306, 2, 24678, 2, 6, 2, 39984, 2, 64662, 2, 6, 2, 104646, 2, 169308, 2, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

From Robert Israel, Jun 07 2018: (Start)

For n >= 4, a(n) = 2 if n is even.

For n >= 7, a(n) == 0 (mod 6) if n is odd.

For n >= 9, a(n) = 6 if n == 3 (mod 6). (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=4, a(6)=2, a(8)=2 are the terms which are coprime to 9 and which occur among {a(1),a(2)...a(8)}. 2 and 4 are the two largest of these terms, so a(9) = 2 + 4 = 6.

MAPLE

N:= 100: # for a(1)..a(N)

V[1]:= 1: V[2]:= 1:

for n from 3 to N do

  Q:= select(t -> igcd(t, n)=1, [seq(V[i], i=1..n-1)]);

  j1:= max[index](Q);

  V[n]:= Q[j1] + max(subsop(j1=NULL, Q))

od:

seq(V[i], i=1..N); # Robert Israel, Jun 07 2018

MATHEMATICA

f[s_] := Append[s, Plus @@ Take[Sort[Select[s, GCD[ #, Length[s] + 1] == 1 &]], -2]]; Nest[f, {1, 1}, 74] (* Ray Chandler, Sep 11 2006 *)

CROSSREFS

Cf. A122456.

Sequence in context: A323407 A073348 A287093 * A319410 A337174 A139770

Adjacent sequences:  A122454 A122455 A122456 * A122458 A122459 A122460

KEYWORD

nonn,look

AUTHOR

Leroy Quet, Sep 07 2006

EXTENSIONS

Corrected and extended by Ray Chandler and Robert G. Wilson v, Sep 11 2006

STATUS

approved

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Last modified August 3 14:40 EDT 2021. Contains 346438 sequences. (Running on oeis4.)