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A084141 a(n) is the index in sequence A084138 when the value of that sequence is one (1), i.e., there is exactly one case where there are exactly a(n) primes between m and 2m, exclusively, for m > 0.

%I A084141 #16 Feb 16 2025 08:32:49
%S A084141 0,22,36,47,79,98,114,134,173,178,184,210,218,221,245,254,262,284,297,
%T A084141 305,327,333,373,387,396,426,459,466,470,484,530,544,563,567,575,587,
%U A084141 616,650,694,700,706,708,737,776,859,881,885,898,926,939,974,993,1002
%N A084141 a(n) is the index in sequence A084138 when the value of that sequence is one (1), i.e., there is exactly one case where there are exactly a(n) primes between m and 2m, exclusively, for m > 0.
%C A084141 This calculation relies on the fact that Pi(2*m) - Pi(m) > m/(3*log(m)) for m >= 5. Conjecture: There are an infinite number of terms in this sequence.
%D A084141 P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.
%H A084141 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate</a>.
%e A084141 a(3)=47 because the 3rd one in sequence A084138 is its item 47. There is exactly one case where there are exactly 47 primes between m and 2m.
%Y A084141 Cf. A060715, A060756, A084138, A084139, A084140, A084142.
%K A084141 nonn
%O A084141 0,2
%A A084141 _Harry J. Smith_, May 15 2003