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 A331125 Numbers k such that there is no prime p between k and (9/8)k, exclusive. 1
 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)
 OFFSET 1,2 COMMENTS 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. REFERENCES David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised edition), Penguin Books, 1997, entry 48, p. 106. LINKS Table of n, a(n) for n=1..21. Robert Breusch, Zur Verallgemeinerung des Bertrandschen Postulates, daß zwischen x und 2x stets Primzahlen liegen, Mathematische Zeitschrift (in German), December 1932, Volume 34, Issue 1, pp. 505-526. Wikipedia, Robert Breusch FORMULA A327802(a(n)) = 0. EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A285586, A327802. Sequence in context: A342441 A129562 A191841 * A318736 A050741 A285710 Adjacent sequences: A331122 A331123 A331124 * A331126 A331127 A331128 KEYWORD nonn,fini,full AUTHOR Bernard Schott, Jan 10 2020 STATUS approved

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Last modified December 7 05:34 EST 2023. Contains 367630 sequences. (Running on oeis4.)