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A077223
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a(1) = 1 and then alternately even and odd numbers not occurring earlier such that the sum of two successive terms is a squarefree number.
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2
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1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 11, 12, 17, 14, 15, 16, 13, 18, 19, 20, 21, 22, 25, 26, 27, 24, 23, 28, 29, 30, 31, 34, 33, 32, 35, 36, 37, 40, 39, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 51, 50, 53, 54, 55, 56, 57, 58, 61, 62, 65, 64, 59, 60, 63, 66, 67, 70, 69, 68, 71, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| No string of 9 successive terms can be consecutive integers simply for one of the sums of pair of terms would be a multiple of 9=3^2. Conjecture: There are infinitely many strings of 8 terms of the form k,k+1,k+2,...k+7. Subsidiary sequences:(1) Start of the strings of 8 consecutive natural numbers. ( 5 more sequences),Start of the strings of r consecutive natural numbers for a particular r, 3<r<8.
A self-inverse permutation of the natural numbers.
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LINKS
| Index entries for sequences that are permutations of the natural numbers
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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PROG
| (Haskell)
import Data.List (find, delete)
import Data.Maybe (fromJust)
a077223 n = a077223_list !! (n-1)
a077223_list = 1 : g 1 [2..] where
g i xs = x : g x (delete x xs) where
x = (fromJust $ find isOddSquarefree $ map (+ i)
isOddSquarefree m = odd m && a008966 m == 1
for_bFile = take 10000 a077223_list
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CROSSREFS
| Cf. A008966.
Sequence in context: A167151 A072275 A122989 * A055265 A117922 A201543
Adjacent sequences: A077220 A077221 A077222 * A077224 A077225 A077226
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KEYWORD
| nice,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 03 2002
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EXTENSIONS
| a(16)-a(71) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 17 2008
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