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A331125
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Numbers k such that there is no prime p between k and (9/8)k, exclusive.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 19, 20, 23, 24, 25, 31, 32, 47
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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In 1932, Robert Hermann Breusch proved that for n >= 48, there is at least one prime p between n and (9/8)n, exclusive (A327802).
The terms of A285586 correspond to numbers k such that there is no prime p between k and (9/8)n, inclusive.
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised edition), Penguin Books, 1997, entry 48, p. 106.
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LINKS
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FORMULA
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EXAMPLE
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Between 16 and (9/8) * 16 = 18, exclusive, there is the prime 17, hence 16 is not a term.
Between 47 and (9/8) * 47 = 52.875, exclusive, 48, 49, 50, 51 and 52 are all composite numbers, hence 47 is a term.
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MATHEMATICA
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Select[Range[47], Count[Range[# + 1, 9# / 8], _?PrimeQ] == 0 &] (* Amiram Eldar, Jan 11 2020 *)
Select[Range[1000], PrimePi[#] == PrimePi[9#/8] &] (* Alonso del Arte, Jan 16 2020 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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