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A103683 a(1)=1, a(2)=2, a(3)=3, a(n) = smallest positive integer not occurring earlier in sequence and coprime to a(n-1), a(n-2) and a(n-3). 6
1, 2, 3, 5, 7, 4, 9, 11, 13, 8, 15, 17, 19, 14, 23, 25, 27, 16, 29, 31, 21, 10, 37, 41, 33, 20, 43, 47, 39, 22, 35, 53, 51, 26, 49, 55, 57, 32, 59, 61, 45, 28, 67, 71, 65, 6, 73, 77, 79, 12, 83, 85, 89, 18, 91, 95, 97, 24, 101, 103, 107, 30, 109, 113, 119, 36, 115, 121, 127, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjectured to be not a permutation of the natural numbers.

Charles R Greathouse IV extended this, and confirms that primes occur in natural order. - Jonathan Vos Post and M. F. Hasler, Jan 18 2011

Conjecture: for n >= 67, a(n) is even if and only if n == 2 mod 4 and divisible by 3 if and only if n == 3 mod 4.  In particular, this implies the last value divisible by 6 is a(66) = 36. - Robert Israel, May 12 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

MAPLE

ina:= proc(n) false end:

a:= proc(n) option remember; local k;

      if n<4 then k:= n

    else for k from 4 while ina(k) or igcd(k, a(n-1))<>1 or

                igcd(k, a(n-2))<>1 or igcd(k, a(n-3))<>1

         do od

      fi; ina(k):= true; k

    end:

seq(a(n), n=1..120);  # Alois P. Heinz, Jan 19 2011

MATHEMATICA

f[s_] := Block[{k = 1, l = Take[s, -3]}, While[ Union[ GCD[k, l]] != {1} || MemberQ[s, k], k++]; Append[s, k]]; Nest[f, {1, 2, 3}, 70] (* Robert G. Wilson v, Jun 26 2011 *)

CROSSREFS

Cf. A084937, A105214.

Sequence in context: A140528 A065037 A101438 * A125151 A273665 A212646

Adjacent sequences:  A103680 A103681 A103682 * A103684 A103685 A103686

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 26 2005

EXTENSIONS

More terms from Robert G. Wilson v, Mar 30 2005

STATUS

approved

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Last modified March 26 00:51 EDT 2017. Contains 284111 sequences.