A072986 - OEIS

%I #15 Jan 09 2021 11:50:34

%S 1,2,6,11,24,52,113,248,553,1245,2828,6481,14963,34770,81253,190836,

%T 450202,1066269,2534269,6042375,14447465,34632759

%N Least k such that Product_{i=1..k} (prime(i) + 1) >= n*Product_{i=1..k} prime(i).

%C Least k such that A054640(k) >= n*A002110(k). - _Michel Marcus_, Jan 09 2021

%F Lim_{n->infinity} a(n+1)/a(n) = e. - _Robert Gerbicz_, May 09 2008

%t a = b = k = 1; Do[ While[a = a*Prime[k]; b = b*(Prime[k] + 1); b < n*a, k++ ]; Print[k]; k++, {n, 1, 16}]

%o (PARI) a(n)=if(n<0,0,s=1; while(prod(i=1,s, prime(i)+1)<prod(i=1,s, prime(i))*n,s++); s);

%Y Cf. A002110, A054640.

%K more,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 14 2002

%E Edited and extended by _Robert G. Wilson v_, Aug 20 2002

%E 6 more terms from _Robert Gerbicz_, May 09 2008