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A259840 a(1)=1, a(2)=2; a(n+2) is the smallest number not occurring earlier such that gcd(a(n),a(n+1)) * gcd(a(n+1),a(n+2)) = a(n+1). 1
1, 2, 4, 6, 3, 5, 10, 8, 12, 9, 15, 20, 16, 28, 7, 11, 22, 14, 21, 18, 24, 44, 33, 27, 36, 32, 40, 25, 30, 42, 35, 45, 54, 48, 56, 49, 63, 72, 64, 88, 55, 50, 60, 66, 77, 70, 80, 104, 13, 17, 34, 26, 39, 51, 68, 52, 65, 75, 90, 78, 91, 84, 96, 136, 85, 95, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Is this a permutation of all natural numbers?

For n>1, gcd(a(n),a(n+1))=1 iff a(n)=prime(2k) and a(n+1)=prime(2k+1).

LINKS

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

MAPLE

b:= proc(n) n>2 end:

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

      if n<3 then n else for k do if b(k) and a(n-1)

        = igcd(a(n-2), a(n-1))*igcd(a(n-1), k) then

          b(k):= false; return k fi od

      fi

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Jul 09 2015

CROSSREFS

Sequence in context: A331522 A075075 A088178 * A161184 A140645 A327724

Adjacent sequences:  A259837 A259838 A259839 * A259841 A259842 A259843

KEYWORD

nonn,look

AUTHOR

Thomas Ordowski, Jul 06 2015

EXTENSIONS

More terms from Alois P. Heinz, Jul 09 2015

STATUS

approved

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Last modified April 8 07:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)