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Search: id:A077223
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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 square-free number. |
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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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CROSSREFS
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Sequence in context: A167151 A072275 A122989 this_sequence A055265 A117922 A073666
Adjacent sequences: A077220 A077221 A077222 this_sequence A077224 A077225 A077226
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KEYWORD
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nice,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 03 2002
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EXTENSIONS
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a(16)-a(71) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 17 2008
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