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 A066805 Least natural number k such that n + sum_{i=1,...,k} Composite[i] is prime, if such k exists; or 0 otherwise. 0
 1, 1, 5, 1, 6, 1, 8, 2, 5, 1, 7, 1, 5, 2, 5, 1, 7, 1, 5, 3, 6, 1, 6, 2, 5, 2, 13, 1, 6, 1, 5, 2, 5, 4, 6, 1, 8, 2, 5, 1, 6, 1, 5, 10, 5, 1, 7, 2, 8, 3, 5, 1, 7, 2, 5, 2, 7, 1, 6, 1, 5, 2, 6, 4, 6, 1, 8, 2, 5, 1, 6, 1, 5, 2, 5, 27, 7, 1, 5, 11, 5, 1, 15, 2, 5, 3, 7, 1, 6, 3, 19, 2, 6, 4, 14, 1, 13, 2, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Is a(n) nonzero for all n? If so, then every n can be represented as the difference of a prime and a partial sum of the composite numbers series. See A066753 for a related possible representation of n as the difference of a prime and a partial sum of the prime numbers series. LINKS EXAMPLE 3 + (1 + 4 + 6 + 8 + 9) = 31, a prime and 5 consecutive composite numbers starting with 1 are required to achieve this. Hence a(3) = 5. CROSSREFS Cf. A066753. Sequence in context: A176320 A190185 A176123 * A028284 A096462 A066948 Adjacent sequences:  A066802 A066803 A066804 * A066806 A066807 A066808 KEYWORD nonn AUTHOR Joseph L. Pe, Jan 19 2002 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jun 12 2002 STATUS approved

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