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, 83212840, 200360193, 483361096, 1168159015, 2827750519

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..27.

Formula

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

a(n) = PrimePi(A072997(n)) = A000720(A072997(n)). - Amiram Eldar, Apr 18 2025

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. A000720, A001113, A002110, A054640, A072997.

Sequence in context: A005673 A084308 A067605 * A079047 A160966 A052326

Adjacent sequences: A072983 A072984 A072985 * A072987 A072988 A072989

Keyword

nonn,more

Author

Benoit Cloitre, Aug 14 2002

Extensions

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

a(17)-a(22) from Robert Gerbicz, May 09 2008

a(23)-a(27) from Amiram Eldar, Apr 18 2025

Status

approved