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

Author

Benoit Cloitre, Aug 14 2002

Keywords

• nonn
• more

Comments

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

Crossrefs

Cf. A000720, A001113, A002110, A054640, A072997.

Programs

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}]

PARI

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

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

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