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.

A111655 n-th composite number appears n-th composite number times.

Original entry on oeis.org

4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15
Offset: 1

Views

Author

Jonathan Vos Post, Aug 12 2005

Keywords

Comments

A002808(n) appears A002808(n) times.

Crossrefs

Cf. A002808, A111653, A111654.

A111653 n-th composite number appears n times.

Original entry on oeis.org

4, 6, 6, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21
Offset: 1

Views

Author

Jonathan Vos Post, Aug 12 2005

Keywords

Comments

A002808(n) appears n times.

Crossrefs

Cf. A002808, A111654, A111655.

Programs

  • Python
    from math import isqrt
from sympy import composite
def A111653(n): return composite(isqrt(n<<3)+1>>1) # Chai Wah Wu, Sep 06 2025

A111656 n-th prime appears n-th composite number times.

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19
Offset: 1

Views

Author

Jonathan Vos Post, Aug 12 2005

Keywords

References

  • T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.

Links

Crossrefs

Cf. A000040, A002808, A111653, A111654, A111655, A111657.

Programs

  • Mathematica
    Module[{nn=20,cm,pr,len},cm=Select[Range[nn],CompositeQ];len = Length[ cm];Table[#[[1]],#[[2]]]&/@Thread[{Prime[Range[len]],cm}]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 06 2018 *)

Formula

A000040(n) appears A002808(n) times.

A111657 n-th composite number appears n-th prime times.

Original entry on oeis.org

4, 4, 6, 6, 6, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15
Offset: 1

Views

Author

Jonathan Vos Post, Aug 12 2005

Keywords

References

  • T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.

Links

Crossrefs

Cf. A000040, A002808, A111653, A111654, A111655, A111656.

Formula

A002808(n) appears A000040(n) times.
Showing 1-4 of 4 results.

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

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