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Search: id:A113593
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| A113593 |
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Minimal differences that appear in arithmetic progressions of primes. |
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+0
1
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| 0, 1, 2, 6, 30, 150, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Collapsed version of sequence A033188. If a conjecture about arithmetic prime progressions is correct (see A033188), this sequence is simply the primorial numbers with 150 inserted into the list. Zero is also included (since p,p is an arithmetic progression with difference 0).
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EXAMPLE
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2 belongs in the sequence because the smallest d satisfying "n, n+d, n+2d are all prime" is 2. 4 does not belong, despite there existing triplets {n, n+4, n+8} that are all prime--because a difference of 4 does not allow a new length of progression, i.e. there is no prime progression {n, n+4, n+8, n+12}.
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CROSSREFS
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Cf. A033188, A034386, A002110.
Sequence in context: A073969 A120950 A055695 this_sequence A122763 A005432 A009422
Adjacent sequences: A113590 A113591 A113592 this_sequence A113594 A113595 A113596
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KEYWORD
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nonn
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AUTHOR
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Jon Wild (wild(AT)music.mcgill.ca), Jan 26 2006
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