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.

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A028683 Pseudo Galois numbers for d=21.

Original entry on oeis.org

1, 420, 81496800, 6988909668048000, 264339188251171547754240000, 4409145118315866486641282521305984000000, 32432910584848683243891703579686352553931989191680000000, 105209765057463921593261518265177017436422522866428383386348592435200000000
Offset: 0

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    FoldList[ #1*21^#2 (21^#2-1)&, 1, Range[ 20 ] ]
    a[n_] := 21^n * Product[21^n - 21^k, {k, 0, n-1}]; Array[a, 8, 0] (* Amiram Eldar, Jul 14 2025 *)
  • PARI
    a(n) = 21^n * prod(k = 0, n-1, 21^n - 21^k); \\ Amiram Eldar, Jul 14 2025

Formula

a(n) = 21^n * Product_{k=0..n-1} (21^n - 21^k).
a(n) ~ c * 21^(n^2+n), where c = Product_{k>=1} (1 - 1/21^k) = 0.950113624091... . - Amiram Eldar, Jul 14 2025

A028686 Pseudo Galois numbers for d=24.

Original entry on oeis.org

1, 552, 182822400, 34935377382604800, 3845511050527581426155520000, 243818371522804938361462294653739991040000, 8904331592711942612922766177589119660252055149215744000000, 187309027227336950425268745082789353880120643944720523727102076558245888000000
Offset: 0

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    FoldList[ #1*24^#2 (24^#2-1)&, 1, Range[ 20 ] ]
    a[n_] := 24^n * Product[24^n - 24^k, {k, 0, n-1}]; Array[a, 8, 0] (* Amiram Eldar, Jul 14 2025 *)
  • PARI
    a(n) = 24^n * prod(k = 0, n-1, 24^n - 24^k); \\ Amiram Eldar, Jul 14 2025

Formula

a(n) = 24^n * Product_{k=0..n-1} (24^n - 24^k).
a(n) ~ c * 24^(n^2+n), where c = Product_{k>=1} (1 - 1/24^k) = 0.956597348026... . - Amiram Eldar, Jul 14 2025

A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.

Original entry on oeis.org

1, 12, 2880, 11612160, 758041804800, 794088208701849600, 13319336815141167562752000, 3575164027575627746190393606144000, 15354978274323252140217954794120612413440000, 1055182047088717407398960909148529544369642384916480000, 1160183823755957350394353874696058298158177597536388268425216000000
Offset: 0

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Keywords

Comments

Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).

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. xii (but beware typos!).

Crossrefs

Programs

  • Maple
    f:=proc(n,eps) local m,d;
    if n mod 2 = 0 then m:=n/2; d:=gcd(4,2^m-eps);
    2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;
    else m:=(n-1)/2;
    2^(m^2)*mul( 4^i-1, i=1..m);
    fi; end;
    [seq(f(n,+1),n=0..20)]
  • Mathematica
    FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]
    a[n_] := 4^n * Product[4^n - 4^k, {k, 0, n-1}]; Array[a, 10, 0] (* Amiram Eldar, Jul 14 2025 *)
  • PARI
    a(n) = 4^n * prod(k = 0, n-1, 4^n - 4^k); \\ Amiram Eldar, Jul 14 2025

Formula

a(n) = 4^n * Product_{k=0..n-1} (4^n - 4^k).
a(n) ~ c * 4^(n^2+n), where c = A100221. - Amiram Eldar, Jul 14 2025

Extensions

Entry revised by N. J. A. Sloane, Dec 30 2008
Duplicate term 1 removed by Amiram Eldar, Jul 14 2025
Previous Showing 11-13 of 13 results.