cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A093435 Duplicate of A048964.

Original entry on oeis.org

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
Offset: 1

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Author

Keywords

A073071 Least k such that k! > prime(1)*prime(2)*...*prime(n) where prime(n) is the n-th prime.

Original entry on oeis.org

3, 4, 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
Offset: 1

Views

Author

Benoit Cloitre, Aug 17 2002

Keywords

Comments

If the greater than sign in the definition is replaced by >=, we get A048964. - R. J. Mathar, May 01 2008

Examples

			n=1: prime(1) = 2, 3! > 2, a(1) = 3.
n=2: prime(1)*prime(2) = 6, 4! > 6, a(2) = 4.

Links

Crossrefs

Cf. A002110, A048964, A135667.

Programs

Formula

a(n) should be asymptotic to C*n (where 1

Extensions

Corrected by Peter Pein (petsie(AT)dordos.net), May 01 2008

A085302 a(n) is the partial sum of A085301(j) from j=1 to n; a(n)-1 shows the number of factorials below n-th primorial.

Original entry on oeis.org

2, 4, 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

Views

Author

Labos Elemer, Jun 26 2003

Keywords

Examples

			For n = 26: a(26) = 34 since there are 33 factorials below the 26th primorial.

Links

Crossrefs

Cf. A085301, A002110, A000142.
Variant of A073071 and A048964.

Programs

  • Mathematica
    fn[n_] := Module[{k = 1, r = n}, While[r >= 1, k++; r /= k]; k - 1]; prim[n_] := Times @@ Prime[Range[n]]; a[1] = 2; a[n_] := fn[prim[n]] + 1; Array[a, 100] (* Amiram Eldar, Feb 09 2025 *)

A093697 Least k so that n! >= primorial(k).

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52, 53, 53, 54, 55, 56, 57
Offset: 1

Views

Author

Robert G. Wilson v, Apr 09 2004

Keywords

Examples

			a(9) = 7 because p#_6 = 30030 < 9! = 362880 < p#_7 = 510510.

Crossrefs

Cf. A048964.

Programs

  • Mathematica
    Primorial[n_] := Product[ Prime[i], {i, n}]; f[n_] := Block[{k = 1}, While[ Primorial[k] < n!, k++ ]; k]; Table[ f[n], {n, 75}]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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