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.

A018074 Powers of fourth root of 10 rounded up.

Original entry on oeis.org

1, 2, 4, 6, 10, 18, 32, 57, 100, 178, 317, 563, 1000, 1779, 3163, 5624, 10000, 17783, 31623, 56235, 100000, 177828, 316228, 562342, 1000000, 1778280, 3162278, 5623414, 10000000, 17782795, 31622777, 56234133, 100000000, 177827942, 316227767, 562341326, 1000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A011007, A017936 (bisection), A308467.

Programs

  • Mathematica
    Ceiling[(Power[10, (4 )^-1])^Range[0,50]]  (* Harvey P. Dale, Mar 18 2011 *)
  • PARI
    a(n) = sqrtnint(10^n-1, 4) + 1; \\ Michel Marcus, Jun 26 2024

Extensions

More terms from Michel Marcus, Aug 21 2019

A018072 Powers of fourth root of 10 rounded down.

Original entry on oeis.org

1, 1, 3, 5, 10, 17, 31, 56, 100, 177, 316, 562, 1000, 1778, 3162, 5623, 10000, 17782, 31622, 56234, 100000, 177827, 316227, 562341, 1000000, 1778279, 3162277, 5623413, 10000000, 17782794, 31622776, 56234132, 100000000, 177827941, 316227766, 562341325, 1000000000, 1778279410
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			a(2) = 3 because 10^(2/4) = 10^(1/2) = sqrt(10) = 3.16228...
a(3) = 5 because 10^(3/4) = 5.62341...
a(4) = 10 because 10^(4/4) = 10^1 = 10.
a(5) = 17 because 10^(5/4) = 17.78279...

Links

Crossrefs

Cf. A017934, A011007, A010467.

Programs

Extensions

A few additional terms from Alonso del Arte, Jan 26 2013

A275358 The difference between A089580(n) and A089579(n).

Original entry on oeis.org

0, 4, 10, 20, 41, 65, 114, 185, 297, 487, 809, 1339, 2253, 3824, 6544, 11297, 19620, 34216, 59926, 105258, 185356, 327039, 577906, 1022466, 1810789, 3209398, 5691825, 10099475, 17927609, 31833805, 56541947, 100449345, 178484340, 317187186, 563744378, 1002052726
Offset: 1

Views

Author

Robert G. Wilson v, Jul 24 2016

Keywords

Comments

Submitted on the request of Omar E. Pol 17 July 2016. (A089579).
a(n) is the sum of A175066(m)-1 over such m that A117453(m)<10^n. - Andrey Zabolotskiy, Aug 17 2016

Examples

			a(2) = A089580(2)-A089579(2) = 4 because of the three terms: 16 = 2^4 = 4^2, 64 = 2^6 = 4^3 = 8^2 and 81 = 3^4 = 9^2; one for 16, two for 64 and one for 81 making a total of 4.

Links

Crossrefs

Cf. A011007, A011557, A070428, A089579, A089580.

Programs

  • Mathematica
    f[n_] := Block[{lim = 10^n -1}, Sum[ (Floor[ lim^(1/k)] - 1)(1 + MoebiusMu[k]), {k, 2, Floor[ Log[2, lim]]}]]; Array[f, 36]

Formula

a(n) = A089580(n) - A089579(n).
Limit_{n->oo} a(n+1)/a(n) = 1.778279... (A011007). - Altug Alkan, Aug 22 2016

A210522 Decimal expansion of 10^(3/4).

Original entry on oeis.org

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

Views

Author

Alonso del Arte, Jan 27 2013

Keywords

Comments

This number is the geometric mean of sqrt(10) and 10.
Floor(10^((4*n - 1)/4)) = A018072(4*n - 1) can be obtained by multiplying this number by 10^(n - 1) and truncating the decimal places.
Harriot gives this constant to 18 decimal places. - Charles R Greathouse IV, Oct 22 2014

Examples

			5.6234132519034908039495103977648...

References

  • P. H. Underwood, "Logarithms" Texas Mathematics Teachers' Bulletin, Vol 6 No. 1 (1920), p. 23.

Links

Crossrefs

Cf. A010467, A011007.

Programs

Showing 1-4 of 4 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.