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 A077223 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. 2
 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; text; internal format)
 OFFSET 1,2 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

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Last modified September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)