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 1-7 of 7 results.

A138946 Positive integers not in A073071.

Original entry on oeis.org

1, 2, 9, 13, 18, 22, 26, 30, 35, 39, 43, 48, 52, 56, 61, 65, 69, 74, 78, 82, 87, 91, 95, 100, 104, 109, 113, 117, 122, 126, 131, 135, 140, 144, 148, 153, 157, 162, 166, 171, 175, 180, 184, 189, 193, 198, 202, 207, 212, 216, 221, 225, 230, 234, 239, 243, 248, 253
Offset: 1

Views

Author

M. F. Hasler, May 02 2008

Keywords

Crossrefs

Cf. A073071, A138945.

Programs

  • PARI
    pp=1;k=0;forprime(p=1,9999,pp*=p;while(k++!<=pp,print1(k"," )))

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

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, 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

Keywords

Comments

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

Examples

			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]

Links

Crossrefs

Cf. A000142, A002110, A073071, A093697.

Programs

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

Extensions

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

A132018 Smallest k such that k! > A058694(n).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 47, 49, 51, 53, 55, 58, 60, 62, 65, 67, 70, 72, 74, 77, 79, 82, 84, 87, 90, 92, 95, 97, 100, 103, 105, 108, 111, 114, 116, 119, 122, 125, 128, 131, 134, 136
Offset: 1

Views

Author

R. J. Mathar, May 01 2008

Keywords

Crossrefs

Cf. A058694, A073071, A137620.

Programs

  • PARI
    smk(n) = {lim = prod(i=1, n, numbpart(i)); k = 0; while (k! <= lim, k++); return (k);} \\ Michel Marcus, Jul 23 2013

A135667 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, 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

Views

Author

Zak Seidov, May 01 2008

Keywords

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

A137620 Smallest k such that k! >= A058694(n).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 47, 49, 51, 53, 55, 58, 60, 62, 65, 67, 70, 72, 74, 77, 79, 82, 84, 87, 90, 92, 95, 97, 100, 103, 105, 108, 111, 114, 116, 119, 122, 125, 128, 131, 134, 136
Offset: 1

Views

Author

R. J. Mathar, May 01 2008

Keywords

Crossrefs

Cf. A058694, A073071, A132018.

A138945 Positive integers not in A132018.

Original entry on oeis.org

1, 9, 12, 15, 17, 20, 22, 24, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 81, 83, 85, 86, 88, 89, 91, 93, 94, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 113, 115, 117, 118, 120, 121, 123
Offset: 1

Views

Author

M. F. Hasler, May 04 2008

Keywords

Comments

Sequence A132018 was motivated by analogy to A073071.
The latter remains quite dense in N: up to 1000 only about every 5th number is missing, which motivated to introduce its complement in N*, A138945.
While A132018 starts in a similar way, it becomes more and more sparse (since A000041 grows much faster); and consequently the present sequence becomes very dense.

Crossrefs

Cf. A132018, A137620, A058694, A073071, A138946, A135667.

Programs

  • PARI
    pp=1;k=0;for(n=1,999,pp*=numbpart(n);while(k++!<=pp,print1(k"," )))

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 *)
Showing 1-7 of 7 results.

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

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