A072986 Least k such that Product_{i=1..k} (prime(i) + 1) >= n*Product_{i=1..k} prime(i).

1, 2, 6, 11, 24, 52, 113, 248, 553, 1245, 2828, 6481, 14963, 34770, 81253, 190836, 450202, 1066269, 2534269, 6042375, 14447465, 34632759

Offset

1,2

Comments

Least k such that A054640(k) >= n*A002110(k). - Michel Marcus, Jan 09 2021

Links

Table of n, a(n) for n=1..22.

Formula

Lim_{n->infinity} a(n+1)/a(n) = e. - Robert Gerbicz, May 09 2008

Mathematica

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}]

Prog

(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);

Crossrefs

Cf. A002110, A054640.

Sequence in context: A005673 A084308 A067605 * A079047 A160966 A052326

Adjacent sequences: A072983 A072984 A072985 * A072987 A072988 A072989

Keyword

more,nonn

Author

Benoit Cloitre, Aug 14 2002

Extensions

Edited and extended by Robert G. Wilson v, Aug 20 2002

6 more terms from Robert Gerbicz, May 09 2008

Status

approved