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.

A004428 Geometric mean of digits of n (rounded down).

Original entry on oeis.org

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

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Author

N. J. A. Sloane

Keywords

Comments

a(n) = 0 for almost all n (in the sense of asymptotic density). - Charles R Greathouse IV, Jan 30 2023

Crossrefs

Cf. A004429, A007954, A257830.

Programs

  • Mathematica
    A004428[n_] := Floor[GeometricMean[IntegerDigits[n]]]
  • PARI
    A004428(n)=sqrtn(prod(i=1,#n=digits(n),n[i]),#n)\1 \\ M. F. Hasler, May 10 2015

A004429 Geometric mean of digits of n (rounded to nearest integer).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A004428, A007954, A257830.

Programs

A257829 The decimal representation of the average of the digits of n starts with the digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 45, 566, 1500, 2250, 3750, 18000, 383333, 4428571, 11250000, 788888888, 1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 44545454545, 358333333333, 4461538461538
Offset: 1

Views

Author

Eric Angelini and Giovanni Resta, May 10 2015

Keywords

Comments

The sequence is infinite since it contains all the numbers m*10^(10^k-1), for 1 <= m <= 9 and k >= 0.

Examples

			566 is a term since the mean of its digits is (5+6+6)/3 = 17/3 and the first 3 digits of 17/3 = 5.6666... are 566. - corrected by _Joseph L. Wetherell_, Mar 17 2018

Links

Crossrefs

Cf. A257830.

Programs

  • Mathematica
    (* outputs terms with at most 100 digits *) sol[nd_] := Block[{z = Range[9 nd]/nd, x}, x = FromDigits /@ First /@ RealDigits[z, 10, nd]; x[[Select[Range@ Length@x, z[[#]] == Mean@ IntegerDigits@x[[#]] &]]]]; Union@ Flatten@Array[sol, 100]

A257294 The first d decimal digits of the geometric mean of the digits of n, where d is the number of digits of n, without leading zeros.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 10, 14, 17, 20, 22, 24, 26, 28, 30, 0, 14, 20, 24, 28, 31, 34, 37, 40, 42, 0, 17, 24, 30, 34, 38, 42, 45, 48, 51, 0, 20, 28, 34, 40, 44, 48, 52, 56, 60, 0, 22, 31, 38, 44, 50, 54, 59, 63, 67, 0, 24, 34, 42, 48, 54, 60, 64, 69, 73, 0, 26, 37, 45, 52, 59, 64
Offset: 0

Views

Author

M. F. Hasler, May 10 2015

Keywords

Comments

Since the geometric mean of the digits of any number is either 0 or between 1 and 9, "the first d digits" is equivalent to the integer part of this value multiplied by 10^(d-1), which leads to the given formula.
Motivated by sequence A257830.

Examples

			For n = 11, a 2-digit number, the geometric mean of the digits is trivially 1, which is 1.000..., and the first two decimal digits are 10, so a(11) = 10. For n=12, geometric mean is sqrt(2) = 1.414..., so a(12) = 14. - _N. J. A. Sloane_, May 11 2015

Crossrefs

Cf. A004428, A004429, A007954, A055642, A257830.

Programs

  • PARI
    a(n)=sqrtn(prod(i=1, #n=digits(n), n[i]), #n)\10^(1-#n)

Formula

a(n) = floor(A007954(n)^(1/A055642(n))*10^(A055642(n)-1))
Showing 1-4 of 4 results.

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

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