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A229832
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First term of smallest sequence of n consecutive weak primes.
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8
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3, 19, 349, 2909, 15377, 128983, 1319411, 17797519, 94097539, 6927837559, 48486712787, 968068681519, 1472840004019, 129001208165719
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OFFSET
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1,1
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COMMENTS
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Erdős called a weak prime A051635 an "early prime," defined to be one which is less than the arithmetic mean of the prime before it and the prime after it. He conjectured that there are infinitely many consecutive pairs of early primes, and offered $100 for a proof and $25000 for a disproof. See Kuperberg 1992.
I make the stronger conjecture that the sequence a(n) is infinite.
a(n) is the prime following A158939(n+1). [Follows from the definitions] - Chris Boyd, Mar 28 2015
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LINKS
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FORMULA
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a(n) = min{p(i): 2*p(i+j) < p(i+j-1) + p(i+j+1), j = 0,1,..,n-1}.
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EXAMPLE
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The primes 19 < (17+23)/2 and 23 < (19+29)/2 are the smallest pair of consecutive weak/early primes, so a(2) = 19.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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