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 1-3 of 3 results.

A376274 Number of prime divisors, counted with multiplicity, of A252043(n), the first n digits of the Champernowne constant.

Original entry on oeis.org

0, 3, 2, 2, 3, 8, 2, 5, 4, 1, 3, 2, 6, 1, 6, 4, 3, 6, 3, 3, 3, 4, 4, 1, 5, 3, 6, 4, 6, 8, 10, 4, 8, 4, 6, 6, 4, 6, 6, 3, 5, 10, 9, 3, 8, 9, 7, 5, 4, 5, 7, 12, 3, 3, 6, 7, 6, 4, 2, 3, 8, 3, 9, 7, 4, 6, 4, 6, 6, 7, 9, 6, 5, 7, 7, 7, 4, 7, 7, 9, 10, 3, 7, 7, 5, 3, 8, 3, 6, 8, 10, 8, 3, 6, 9, 7, 8, 7, 14, 4
Offset: 1

Views

Author

Scott R. Shannon, Sep 18 2024

Keywords

Examples

			a(6) = 8 as A252043(6) = 123456 = 2^6 * 3 * 643, which has 8 prime divisors.

Crossrefs

Cf. A252043, A033307, A176942, A001222.

Programs

  • Mathematica
    Lim=65;ch=RealDigits[ChampernowneNumber[], 10, Lim][[1]];Table[PrimeOmega[FromDigits[Take[ch,n]]],{n,Lim}] (* James C. McMahon, Sep 19 2024 *)

Formula

a(n) = A001222(A252043(n)).

A376545 Least prime factor of A252043(n) for n > 1 with a(1) = 1.

Original entry on oeis.org

1, 2, 3, 2, 3, 2, 127, 2, 3, 1234567891, 2, 9091, 3, 12345678910111, 2, 17, 113, 7, 2, 19, 3, 7, 2, 123456789101112131415161, 3, 13, 2, 17, 13, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 29, 547, 2, 3, 3, 3, 2, 31, 3, 3, 2, 3, 71, 7
Offset: 1

Views

Author

Jean-Marc Rebert, Sep 27 2024

Keywords

Examples

			A252043(3) = 123 = 3 * 41, so a(3) = 3.

Links

Crossrefs

Cf. A020639, A252043, A376274.

Programs

  • PARI
    a(n) = my(list=List(), k=1); while(#listMichel Marcus, Sep 29 2024

Formula

a(n) = A020639(A252043(n)).

A345672 a(n) is the least m such that the decimal expansion of n appears in the concatenation of m, ..., m+k for some k >= 0 and Sum_{i = m..m+k-1} A055642(i) < A055642(n) <= Sum_{i = m..m+k} A055642(i).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 20, 12, 22, 2, 24, 25, 26, 27, 28, 29, 30, 13, 23, 33, 3, 35, 36, 37, 38, 39, 40, 14, 24, 34, 44, 4, 46, 47, 48, 49, 50, 15, 25, 35, 45, 55, 5, 57, 58, 59, 60, 16, 26, 36, 46, 56, 66, 6, 68
Offset: 0

Views

Author

Rémy Sigrist, Jun 22 2021

Keywords

Comments

This sequence is similar to A055642; here we consider decimal expansions, there binary expansions.

Examples

			For n = 21:
- the decimal expansion of 21 first appears in the concatenation of 12 and 13,
- so a(21) = 12.

Links

Crossrefs

Cf. A007376, A055642, A083653 (binary analog), A252043.

Programs

  • PARI
    See Links section.

Formula

a(n) <= n.
a(n) = 1 iff n belongs to A252043.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.