A048964 a(n) is smallest number k such that k! >= n-th primorial number (A002110(n)).

2, 3, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 92, 93

Offset

1,1

Comments

If in the definition '>=' is replaced by '>' we get A073071. - Bernard Schott, Feb 20 2021

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

9! = 362880 < A002110(7) = 2*3*5*7*11*13*17 = 510510 <= 10! = 3628800, so a(7)=10. [edited by Jon E. Schoenfield, May 13 2018]

Mathematica

Primorial[n_] := Product[ Prime[i], {i, n}]; a[n_] := Block[{k = 1}, While[(k!) < Primorial[n], k++ ]; k]; Table[ a[n], {n, 71}] (* Robert G. Wilson v, Apr 09 2004 *)
Module[{nn=100, pn, k=2}, pn=FoldList[Times, Prime[Range[nn]]]; Table[ While[ k!< pn[[n]], k++]; k, {n, nn}]] (* Harvey P. Dale, Dec 12 2018 *)

Prog

(PARI) a(n) = {my(pr = prod(k=1, n, prime(k)), k = 0); while (k! < pr, k++); k; } \\ Michel Marcus, May 14 2018

Crossrefs

Cf. A000142, A002110, A073071, A093697.

Sequence in context: A287770 A039080 A093435 * A028749 A028764 A366319

Adjacent sequences: A048961 A048962 A048963 * A048965 A048966 A048967

Keyword

nonn

Author

Labos Elemer

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007

Status

approved