A161847 - OEIS

%I #15 Oct 07 2024 01:05:55

%S 2,3,1,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277

%N Denominator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).

%C Conjecture: the sequence (prime((n+1)^2) - prime(n^2))/prime(n) converges to 4.

%F a(n) = denominator((A011757(n+1) - A011757(n))/A000040(n)). - _Petros Hadjicostas_, May 13 2020

%e The first few fractions are 5/2, 16/3, 6/1, 44/7, 54/11, ... = A161846/A161847.

%o (PARI) a(n) = denominator((prime((n+1)^2) - prime(n^2))/prime(n)); \\ _Michel Marcus_, May 14 2020

%Y Cf. A000040, A011757, A161846 (numerators).

%K nonn,frac,changed

%O 1,1

%A _Daniel Tisdale_, Jun 20 2009

%E Keyword:frac added by _R. J. Mathar_, Jun 30 2009

%E Extended by _Ray Chandler_, May 06 2010

%E Various sections edited by _Petros Hadjicostas_, May 13 2020