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Search: id:A106639
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| 2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43, 59, 61, 67, 83, 157, 173, 227, 277, 283, 317, 347, 563, 653, 733, 787, 877, 907, 997, 1213, 1237, 1283, 1307, 1523, 1867, 2083, 2693, 2797, 2803, 3253, 3413, 3517, 3643, 3677, 3733, 3803, 4253, 4363, 4547, 4723, 5387
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OFFSET
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0,1
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COMMENT
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Primes are distinguished among the integers by having the fewest possible divisors. Among the primes, which primes are similarly distinguished? The distinguished primes have the fewest possible divisors in the neighborhood. Specifically, p is a distinguished prime iff together p-1, p, and p+1, have 7 or fewer prime factors, counting multiple factors. Of course, the definition could be adjusted to make 3, or even 2, the unique distinguished prime, but then the sequence of distinguished primes would be severly truncated.
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EXAMPLE
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19 is in the sequence because 18 has 3 prime factors, 2, 3, and 3,
19 has 1, and 20 has 3 prime factors, 2, 2, and 5, for a total of 7 prime factors in the neighborhood.
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CROSSREFS
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Cf. A000040.
Adjacent sequences: A106636 A106637 A106638 this_sequence A106640 A106641 A106642
Sequence in context: A049643 A050437 A096246 this_sequence A078334 A108696 A092581
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KEYWORD
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nonn
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AUTHOR
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Walter Nissen (wnissen(AT)tfn.net), May 11 2005
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