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A089781
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Successive coprime numbers with distinct successive differences: gcd(a(k+1),a(k)) = gcd(a(m+1),a(m)) = 1 and a(k+1)-a(k) = a(m+1)-a(m) <==> m=k.
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4
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1, 2, 5, 7, 11, 16, 23, 29, 37, 46, 57, 67, 79, 92, 107, 121, 137, 154, 173, 191, 211, 232, 255, 277, 301, 326, 353, 379, 407, 436, 467, 497, 529, 562, 597, 631, 667, 704, 743, 781, 821, 862, 905, 947, 991, 1036, 1083, 1129, 1177, 1226, 1277
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OFFSET
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1,2
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COMMENTS
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Conjecture: If a(k+1)-a(k) = n then k < C*n. Can someone find an estimate for the constant C?
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LINKS
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FORMULA
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a(n+1) = a(n) + (smallest number coprime with a(n) and not already added). - Reinhard Zumkeller, Aug 15 2015
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EXAMPLE
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5 follows 2 as 4 is not coprime to 2 and 5-2 = 3, 2-1 = 1.
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PROG
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(Haskell)
import Data.List (delete)
a089781 n = a089781_list !! (n-1)
a089781_list = 1 : f [1..] 1 where
f xs y = g xs where
g (z:zs) = if gcd y z == 1 then y' : f (delete z xs) y' else g zs
where y' = y + z
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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