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.

A083379 a(n) = the number of squares with at most n digits and first digit 1.

Original entry on oeis.org

1, 2, 7, 20, 62, 193, 608, 1918, 6061, 19160, 60582, 191568, 605782, 1915640, 6057776, 19156359, 60577716, 191563545, 605777108, 1915635402
Offset: 1

Views

Author

Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

Keywords

Comments

Asymptotically, the probability that a square begins with 1 is (sqrt(2)-1)/(sqrt(10)-1).
A generalization to arbitrary powers is found in Hürlimann, 2004. As the power increases, the probability distribution approaches Benford's law.

Links

Crossrefs

Cf. A083377, A083378, A083380.

Programs

  • Maple
    ListTools:-PartialSums([seq(floor(sqrt(2*10^n))-ceil(sqrt(10^n))+1, n=0..20)]); # Robert Israel, Feb 15 2021

Extensions

Edited by Don Reble, Nov 05 2005

A083378 a(n) is the largest integer whose cube has n digits and first digit 1, except that a(2)=2.

Original entry on oeis.org

1, 2, 5, 12, 27, 58, 125, 271, 584, 1259, 2714, 5848, 12599, 27144, 58480, 125992, 271441, 584803, 1259921, 2714417, 5848035, 12599210, 27144176, 58480354, 125992104, 271441761, 584803547, 1259921049, 2714417616, 5848035476
Offset: 1

Views

Author

Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

Keywords

Comments

a(2)=2 because there is no integer with cube between 10 and 19.
A generalization to arbitrary powers is found in Hürlimann, 2004.

Links

Crossrefs

Cf. A061439, A083377, A083379, A083380.

Programs

  • Mathematica
    Floor[Power[(10^Range[30])/5, (3)^-1]] (* Harvey P. Dale, Jul 15 2011 *)

Formula

a(n) = floor((10^n/5)^(1/3)).

Extensions

Edited by Don Reble, Nov 05 2005

A083380 a(n) is the number of cubes with at most n digits and first digit 1.

Original entry on oeis.org

1, 1, 2, 5, 11, 23, 49, 105, 225, 485, 1045, 2252, 4852, 10452, 22517, 48510, 104508, 225153, 485075, 1045058, 2251505, 4850716, 10450546, 22515012, 48507117, 104505409, 225150073, 485071123, 1045054049, 2251500692
Offset: 1

Views

Author

Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

Keywords

Comments

Asymptotically, the probability that a cube begins with 1 is (2^(1/3) - 1)/(10^(1/3) - 1).
A generalization to arbitrary powers is found in Hürlimann, 2004. As the power increases, the probability distribution approaches Benford's law.

Links

Crossrefs

Cf. A083377, A083378, A083379.

Extensions

Edited by Don Reble, Nov 05 2005
Showing 1-3 of 3 results.

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

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