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A251554
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a(1)=1, a(2)=2, a(3)=5; thereafter a(n) is the smallest number not occurring earlier having at least one common factor with a(n-2), but none with a(n-1).
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3
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1, 2, 5, 4, 15, 8, 3, 10, 9, 14, 27, 7, 6, 35, 12, 25, 16, 45, 22, 21, 11, 18, 55, 24, 65, 28, 13, 20, 39, 32, 33, 26, 51, 38, 17, 19, 34, 57, 40, 63, 44, 49, 30, 77, 36, 91, 46, 105, 23, 42, 115, 48, 85, 52, 75, 56, 69, 50, 81, 58, 93, 29, 31, 87, 62, 99, 64, 111
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OFFSET
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1,2
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COMMENTS
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A variant of A098550. See that entry for much more information.
It seems likely that this sequence will never merge with A098550, but it would be nice to have a proof.
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LINKS
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MATHEMATICA
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a251554[lst_List] :=
Block[{k = 3},
While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 ||
MemberQ[lst, k], k++]; Append[lst, k]]; Nest[a251554, {1, 2,
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PROG
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(Python)
from fractions import gcd
A251554_list, l1, l2, s, b = [1, 2, 5], 5, 2, 3, {5}
for _ in range(10**4):
....i = s
....while True:
........if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
............l2, l1 = l1, i
............b.add(i)
............while s in b:
................b.remove(s)
................s += 1
............break
(Haskell)
import Data.List (delete)
a251554 n = a251554_list !! (n-1)
a251554_list = 1 : 2 : 5 : f 2 5 (3 : 4 : [6..]) where
f u v ws = g ws where
g (x:xs) = if gcd x u > 1 && gcd x v == 1
then x : f v x (delete x ws) else g xs
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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