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A075573
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a(1)=1; a(n) is the smallest positive number not occurring earlier, with different parity from a(n-1), such that sum of any subsequence of two or more consecutive terms is composite.
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1
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1, 8, 7, 18, 15, 6, 3, 36, 21, 30, 9, 16, 5, 44, 25, 24, 27, 60, 39, 42, 33, 66, 69, 26, 37, 48, 57, 12, 51, 14, 49, 84, 63, 90, 99, 120, 81, 126, 29, 4, 95, 22, 93, 102, 129, 72, 75, 132, 111, 108, 45, 96, 141, 114, 105, 150, 171, 54, 135, 168, 123, 78, 177, 144, 117
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OFFSET
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0,2
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COMMENTS
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The sequence is infinite. To extend it from the first N terms, one seeks a constellation of composite numbers, of the right parity, whose span is no greater than the sum of the first N terms, S(N). There are infinitely many sequences, of consecutive composite numbers, of length S(N)+1 (indeed, any particular length); and each of those contains a sequence of length S(N) with the right parity. One of those must suffice and that puts an upper-bound on the N+1'st term. - Don Reble, Oct 02 2002
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LINKS
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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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