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A110924 a(1) = 1, a(2) = 2; a(n) is smallest positive integer not among earlier terms of the sequence such that gcd(a(n), a(n-1) + a(n-2)) = 1. 1
1, 2, 4, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 3, 9, 35, 15, 21, 41, 27, 33, 43, 39, 45, 47, 49, 53, 55, 59, 61, 67, 51, 57, 65, 63, 69, 71, 73, 77, 79, 83, 85, 89, 91, 97, 75, 81, 95, 87, 93, 101, 99, 103, 105, 107, 109, 113, 115, 119, 121, 127, 111, 117, 125, 123, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

2 and 4 are the only even terms in the sequence. Is every odd positive integer in the sequence?

LINKS

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

EXAMPLE

Of the positive integers not among the first 4 terms of the sequence, 7 is the smallest which is coprime to a(3) + a(4) = 4 + 5 = 9.

MAPLE

N:= 1000: # to get the first N terms

LCp:= proc(c, R, q)

local T, TM, m;

T:= select(t -> igcd(t, q) = 1, {$1 .. q-1});

m:= floor(c/q);

T:= map(`+`, T, m*q);

TM:= T minus R minus {$m*q .. c};

while TM = {} do

  T:= map(`+`, T, q);

  TM := T minus R;

od:

min(TM);

end proc;

A110924[1]:= 1: A110924[2]:= 2: A110924[3]:= 4: A110924[4]:= 5:

c:= 1: R:= {2, 4, 5}:

for n from 5 to N do

  A110924[n]:= LCp(c, R, A110924[n-1] + A110924[n-2]);

  if A110924[n] = c+2 then

    c:= c+2;

    while member(c+2, R) do c:= c+2 od:

    R:= select(`>`, R, c);

  else

    R:= R union {A110924[n]}

  fi;

od:

seq(A110924[n], n=1..N); # Robert Israel, May 09 2014

MATHEMATICA

a[1] = 1; a[2] = 2; a[3] = 4;

a[n_] := a[n] = Module[{aa = Array[a, n-1], b = a[n-1] + a[n-2]}, For[k = 3, True, k += 2, If[FreeQ[aa, k], If[CoprimeQ[k, b], Return[k]]]]];

Array[a, 100] (* Jean-Fran├žois Alcover, Aug 26 2020 *)

PROG

(PARI) { u=[2, 1]; c=3; s=u[1]+u[2]; m=Set(); m=setunion(m, [1]); m=setunion(m, [2]); print1(1, ", ", 2); for(k=1, 100, i=2; while(gcd(i, s)>1 || setsearch(m, i)!=0, i++); u[(c%2)+1] = i; c++; s=u[1]+u[2]; m=setunion(m, [i]); print1(i, ", ")) } \\ Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005

CROSSREFS

Sequence in context: A147991 A033160 A350147 * A335402 A192590 A028289

Adjacent sequences:  A110921 A110922 A110923 * A110925 A110926 A110927

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 23 2005

EXTENSIONS

More terms from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005

STATUS

approved

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Last modified September 28 11:24 EDT 2022. Contains 357070 sequences. (Running on oeis4.)