A084141 - OEIS

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 #15 Feb 24 2023 11:26:09

%S 0,22,36,47,79,98,114,134,173,178,184,210,218,221,245,254,262,284,297,

%T 305,327,333,373,387,396,426,459,466,470,484,530,544,563,567,575,587,

%U 616,650,694,700,706,708,737,776,859,881,885,898,926,939,974,993,1002

%N 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 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 P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate</a>.

%e 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 Cf. A060715, A060756, A084138, A084139, A084140, A084142.

%K nonn

%O 0,2

%A _Harry J. Smith_, May 15 2003