A077223 a(1) = 1 and then alternately even and odd numbers not occurring earlier such that the sum of any two successive terms is a squarefree number.

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

Offset

1,2

Comments

No string of 9 successive terms can be consecutive integers simply because 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.

Possible subsidiary sequences: Start of the strings of 8 consecutive natural numbers. Start of the strings of r consecutive natural numbers for a particular r, 3 < r < 8.

A self-inverse permutation of the natural numbers.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

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

Crossrefs

Cf. A008966.

Sequence in context: A321726 A353829 A267299 * A265369 A267308 A264965

Adjacent sequences: A077220 A077221 A077222 * A077224 A077225 A077226

Keyword

nice,nonn

Author

Amarnath Murthy, Nov 03 2002

Extensions

a(16)-a(71) from Donovan Johnson, Nov 17 2008

Status

approved