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.

A004231 Ackermann's sequence: n^^n := n^n^n^...^n (with n n's).

Original entry on oeis.org

1, 1, 4, 7625597484987
Offset: 0

Views

Author

Daniel Wild (wild(AT)edumath.u-strasbg.fr)

Keywords

Comments

Using Knuth's arrow notation, this is n^^^2 (n-penta-2) or n^^n (n-tetra-n). - Andrew Robbins, Apr 16 2009
Comment from Trevor Green: The fourth term in this sequence has about as many digits - 8.07 * 10^153 - as the *square* of the number of protons in the universe.
We could prepend a(0) = 1 (since 0^^0 = 1, that is, the "empty power tower" gives the "empty product"). - Daniel Forgues, May 17 2013
The last 60 decimal digits of a(4) are ...67586985427238232605843019607448189676936860456095261392896. - Daniel Forgues, Jun 25 2016
From Daniel Forgues, Jul 06 2016: (Start)
a(4) has (the following number having 154 decimal digits)
80723047260282253793826303970853990300713679217387 \
43031867082828418414481568309149198911814701229483 \
451981557574771156496457238535299087481244990261351117 decimal digits.
a(4) = 4^4^4^4 = 4^
13407807929942597099574024998205846127479365820592 \
39337772356144372176403007354697680187429816690342 \
7690031858186486050853753882811946569946433649006084096,
the exponent of 4 having 155 decimal digits. (End)
The fractional part of 4^4^4*log[10](4) starts .373100157363599870..., so the first few digits of a(4) are 23610226714597313.... - Robert Israel, Jul 06 2016

References

  • John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 60.

Links

Crossrefs

Cf. A027747, A008868 (which mentions an older estimate for the same number), A266200.
Main diagonal of A321312.

Programs

  • Maple
    b:= (n, i)-> `if`(i=0, 1, n^b(n, i-1)):
a:= n-> b(n, n):
seq(a(n), n=0..3);  # Alois P. Heinz, Aug 22 2017
  • Mathematica
    a[n_] := If[n == 0, 1, Nest[n^#&, n, n-1]];
Table[a[n], {n, 0, 3}] (* Jean-François Alcover, Mar 19 2019 *)

A003133 Order of simple Chevalley group E_8(2).

Original entry on oeis.org

3, 3, 7, 8, 0, 4, 7, 5, 3, 1, 4, 3, 6, 3, 4, 8, 0, 6, 2, 6, 1, 3, 8, 8, 1, 9, 0, 6, 1, 4, 0, 8, 5, 5, 9, 5, 0, 7, 9, 9, 9, 1, 6, 9, 2, 2, 4, 2, 4, 6, 7, 6, 5, 1, 5, 7, 6, 1, 6, 0, 9, 5, 9, 9, 0, 9, 0, 6, 8, 8, 0, 0, 0, 0, 0
Offset: 75

Views

Author

N. J. A. Sloane

Keywords

Examples

			337804753143634806261388190614085595079991692242467651576160959909068800000.

References

  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

Crossrefs

Cf. A008868.

Programs

  • Maple
    2^120*(2^2-1)*(2^8-1)*(2^12-1)*(2^14-1)*(2^18-1)*(2^20-1)*(2^24-1)*(2^30-1);

A178798 Expansion of the polynomial x^36*(x^12-1)*(x^9+1)*(x^8-1)*(x^6-1)*(x^5-1)*(x^2-1) in increasing powers of x.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 1, -1, 0, -1, -1, 0, 1, 0, -1, 2, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -2, 1, 0, -1, 0, 1, 1, 0, 1, -1, -1, 0, 0, -1, 0, 1
Offset: 0

Views

Author

N. J. A. Sloane, Dec 26 2010

Keywords

Comments

x^36*(x^12-1)*(x^9+1)*(x^8-1)*(x^6-1)*(x^5-1)*(x^2-1) is the order of the twisted Chevalley group 2_E_6 (q), q = prime power.

References

  • R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.

Crossrefs

Cf. A008915, A008868, A178795.
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.