A135667 Least k such that k!! > prime(1)*prime(2)*...*prime(n) where prime(n) is the n-th prime.

3, 4, 6, 8, 10, 12, 14, 16, 19, 21, 23, 25, 28, 30, 32, 34, 37, 39, 41, 43, 46, 48, 50, 52, 55, 57, 59, 62, 64, 66, 68, 71, 73, 75, 78, 80, 82, 84, 87, 89, 91, 94, 96, 98, 101, 103, 105, 108, 110, 112, 114, 117, 119, 121, 124, 126, 128, 131, 133, 135, 138

Offset: 1

Author

Zak Seidov, May 01 2008

Keywords

• nonn

Crossrefs

Cf. A002110, A006882, A073071.

Programs

Mathematica

With[{prml=FoldList[Times,Prime[Range[70]]]},Table[Module[{k=1},While[k!!<=prml[[n]],k++];k],{n,70}]] (* Harvey P. Dale, Jul 08 2025 *)

PARI

dbf(n) = prod(i = 0, floor((n-1)/2), n - 2*i );
a(n) = pr = prod(i = 1, n, prime(i)); k = 1; while(dbf(k) <= pr, k++); k; \\ Michel Marcus, Oct 13 2013

Extensions

More terms from Michel Marcus, Oct 13 2013