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

2, 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, 140

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= proc(n) option remember; local k;
      for k from a(n-1) while doublefactorial(k)<=p(n) do od; k
    end: a(-1):=0:
seq(a(n), n=0..68);

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 *)

Prog

(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

Crossrefs

Cf. A002110, A006882, A073071.

Sequence in context: A283808 A068578 A203812 * A047894 A113769 A056865

Adjacent sequences: A135664 A135665 A135666 * A135668 A135669 A135670

Keyword

nonn

Author

Zak Seidov, May 01 2008

Extensions

More terms from Michel Marcus, Oct 13 2013

a(0)=2 prepended by Alois P. Heinz, Mar 11 2026

Status

approved