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%I A331125 #37 Jan 17 2020 04:22:21
%S A331125 1,2,3,4,5,6,7,8,9,11,13,14,15,19,20,23,24,25,31,32,47
%N A331125 Numbers k such that there is no prime p between k and (9/8)k, exclusive.
%C A331125 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).
%C A331125 The terms of A285586 correspond to numbers k such that there is no prime p between k and (9/8)n, inclusive.
%D A331125 David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised edition), Penguin Books, 1997, entry 48, p. 106.
%H A331125 Robert Breusch, <a href="https://doi.org/10.1007/BF01180606"> Zur Verallgemeinerung des Bertrandschen Postulates, daß zwischen x und 2x stets Primzahlen liegen</a>, Mathematische Zeitschrift (in German), December 1932, Volume 34, Issue 1, pp. 505-526.
%H A331125 Wikipedia, <a href="https://en.wikipedia.org/wiki/Robert_Breusch">Robert Breusch</a>
%F A331125 A327802(a(n)) = 0.
%e A331125 Between 16 and (9/8) * 16 = 18, exclusive, there is the prime 17, hence 16 is not a term.
%e A331125 Between 47 and (9/8) * 47 = 52.875, exclusive, 48, 49, 50, 51 and 52 are all composite numbers, hence 47 is a term.
%t A331125 Select[Range[47], Count[Range[# + 1, 9# / 8], _?PrimeQ] == 0 &] (* _Amiram Eldar_, Jan 11 2020 *)
%t A331125 Select[Range[1000], PrimePi[#] == PrimePi[9#/8] &] (* _Alonso del Arte_, Jan 16 2020 *)
%Y A331125 Cf. A285586, A327802.
%K A331125 nonn,fini,full
%O A331125 1,2
%A A331125 _Bernard Schott_, Jan 10 2020

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