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A066818
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a(n) = least natural number k such that n + sum_{i=1,...,k} Sophie_Germain[i] is prime, if such k exists; = 0 otherwise.
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0
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1, 2, 1, 12, 1, 2, 3, 2, 1, 4, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 4, 5, 2, 7, 2, 1, 6, 1, 6, 3, 2, 3, 6, 1, 2, 3, 2, 1, 4, 1, 2, 3, 8, 1, 4, 11, 2, 3, 4, 1, 4, 7, 2, 13, 2, 1, 4, 1, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sophie_Germain[i] denotes the i-th Sophie Germain prime (A005384).
There is some empirical evidence to suggest a(n) is nonzero for every n. That is, every n can be expressed as the difference between a prime and a partial sum of the Sophie Germain primes series. See A066753 for a similar conjecture.
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EXAMPLE
| 7 + (2 + 3 + 5) = 17, a prime and three consecutive Sophie Germain primes starting from 2, the first Sophie Germain prime, are needed to achieve this. So a(7) = 3.
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CROSSREFS
| Cf. A005384, A066753.
Sequence in context: A074956 A176088 A069566 * A005730 A112284 A167401
Adjacent sequences: A066815 A066816 A066817 * A066819 A066820 A066821
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 19 2002
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